IMPACT OF ELECTRICAL CONTACTING SCHEME ON

PERFORMANCE OF InGaN/GaN SCHOTTKY SOLAR CELLS

Aditya Jain

Thesis submitted to the faculty of the Virginia Polytechnic Institute and State University

in partial fulfillment of the requirements for the degree of

Master of Science

In

Electrical Engineering

Louis J. Guido

Guo-Quan Lu

Paul Plassmann

Mariusz K. Orlowski

August 14, 2014

Blacksburg, VA

Keywords: Transparent conductive layer, Schottky solar cell, Device characterization

Copyright © 2014, Aditya Jain

IMPACT OF ELECTRICAL CONTACTING SCHEME ON

PERFORMANCE OF InGaN/GaN SCHOTTKY SOLAR CELLS

Aditya Jain

ABSTRACT

Realization of low-resistance electrical contacts on both sides of a solar cell is essential for

obtaining the best possible performance. A key component of a solar cell is a metal contact

on the illuminated side of the cell which should efficiently collect carriers. These contacts

can be formed using an opaque metal grid/finger pattern. The metal electrode may be used

alone or in combination with a broad-area transparent conductive film. This work aims at

investigating the impact of the electrical contacting scheme employed in InGaN/GaN

Schottky barrier solar cells on their performance. InGaN is a III-V compound

semiconductor and has a tunable direct band-gap (0.7 eV to 3.4 eV) which spans most of

the solar spectrum; this fact, along with other beneficial material properties, motivates the

study of InGaN photovoltaic devices. A number of groups have recently investigated

InGaN-based homo-junction and hetero-junction p-i-n solar cells. However, very few

groups have worked on InGaN Schottky solar cells. Compared to p-n junctions, Schottky

barrier solar cells are cheaper to grow and fabricate; they are also expected to improve the

spectral response because of near surface depletion regions in the shorter wavelength

regions. In this particular work on InGaN based solar cells, a Schottky diode structure was

used to avoid the issue of highly resistive p-type InGaN. In this study, platinum (Pt) is used

to form a Schottky barrier with an InGaN/GaN absorber region. Electrical and optical

properties of platinum films are investigated as a function of their thickness. InGaN/GaN

Schottky solar cells with platinum as the transparent conductive film are reported and their

performance is evaluated as a function of the metal thickness.

iii

Dedication

Dedicated to my family, who always believed in me,

For their love and support.

To those who have inspired and motivated me.

To those who find joy in the thrill of creative effort.

iv

Acknowledgements

I am deeply grateful to my advisor, Dr. Louis Guido, for his academic guidance and keen

support over the last two years. I appreciate the time and effort that he has put in to our

discussions and meetings; going as far as making time on the weekends. I will always be

thankful to him for giving me an opportunity to work with him. I have learned a lot from

him during my time here, a lot of which goes beyond the research aspect. I am thankful to

Dr. G. Q Lu, Dr. Paul Plassmann and Dr. Marius Orlowski for serving on my committee;

and for providing valuable insights on various issues relating to my thesis. A special thanks

to Dr. Paul Plassmann for guiding me in the right direction when I needed it the most.

I would like to thank other members of Dr. Guido’s research group for their help and

support which includes: Kevin, Noah, David, Tim, Eric and Rachel. In particular, I would

like to thank Kevin who has been an excellent mentor and guide. Kevin’s guidance was

extremely helpful, especially in the beginning, when I was completely new to this field of

research. I would also like to thank Donald Leber for his assistance in using the Micron

cleanroom facilities. I would like to thank all my teachers who have greatly enriched my

learning experience here at Virginia Tech. I would also like to thank my ECE academic

advisor, Ms. Mary Brewer for always giving me valuable advice right from my time here

as an undergraduate student. I am grateful to the Graduate School and Cranwell

International Center for all their help and support. I would also like to thank all my friends

for their support, who have made my time here, memorable.

v

I am deeply grateful to my entire family to whom I dedicate this thesis. My grandfather,

Late Ravish Chandra Jain has been a source of great inspiration. I would like to thank my

grandmother, Kusum Jain who has been extremely supportive and motivating. I would like

to thank my mother, Sandhya Jain who has been a constant source of encouragement and

love. I would like to thank my father, Anuj Jain for his relentless support and faith in my

abilities. Heartfelt thanks to my sister, Vasudha Jain, her husband, Gaurav Jain and their

daughter, Devina Jain for their continued love and support. I would also like to thank my

relatives and extended family here in the US who have been very supportive and helpful

as well.

Although this thesis represents the work I did for my masters degree, it cannot express the

long hours spent in lab, the joy of learning new things, the hope for good results and the

sadness followed by each failed attempt. However, each attempt presented an opportunity

to learn something new and it helped me appreciate the subject matter even more. Lastly,

I would like to thank Virginia Tech for providing a congenial and supportive environment

for learning; and for the memories that I will cherish forever.

vi

Table of Contents

Abstract .............................................................................................................................. ii

Dedication ......................................................................................................................... iii

Acknowledgements ......................................................................................................... iv

List of Figures ................................................................................................................. viii

List of Tables ................................................................................................................... xii

Chapter 1. Introduction .................................................................................................... 1

1.1 Harnessing the power of the sun ......................................................................... 1

1.2 Brief History and State of the Art of Solar Cells .................................................. 3

1.3 Indium Gallium Nitride Solar Cell ....................................................................... 8

1.3.1 InGaN Material System ................................................................................ 8

1.3.2 Research Progress in InGaN Solar Cells ..................................................... 10

1.3.3 Challenges with InGaN Solar Cells ............................................................ 11

1.4 Research Objectives ........................................................................................... 12

1.5 Organization of Thesis ....................................................................................... 14

Chapter 2. Schottky Barrier Solar Cells: Principles of Operation ............................... 15

2.1 Theory of P-N Junction Solar Cells .................................................................... 15

2.2 Theory of Schottky Barrier Solar Cells............................................................... 22

2.3 Solar Cells with Transparent Conducting Films ............................................... 24

2.4 Metal-Semiconductor Contacts ......................................................................... 25

2.5 Absorption and Transmission in Thin Films ..................................................... 27

Chapter 3. Characterization of Transparent Conducting Films ................................. 30

3.1 Transfer Length Measurements (TLM) ............................................................. 30

3.2 Transmission and Reflection Measurements ..................................................... 33

3.3 Data Analysis and Discussion ............................................................................ 34

3.3.1 TLM Results ............................................................................................... 34

3.3.2 Optical Results ........................................................................................... 39

3.3.3 Summary of Results .................................................................................... 40

Chapter 4. Solar Cell Characterization ......................................................................... 42

4.1 Solar Cell Structure ............................................................................................ 42

4.2 Crosslight APSYS Simulation ............................................................................ 46

4.3 Characterization ................................................................................................ 51

vii

4.3.1 Dark & Illuminated I-V Measurements ..................................................... 51

4.3.2 Sources of Error .......................................................................................... 51

4.4 Experimental Results ......................................................................................... 56

4.5 Data Analysis and Discussion ............................................................................ 61

Chapter 5. Summary and Conclusions .......................................................................... 69

Appendix A. I-V Measurement Setup ........................................................................... 72

REFERENCES ................................................................................................................. 74

viii

List of Figures

Figure 1.1 World Energy Consumption (1990-2040) ..................................................................... 2

Figure 1.2 Recent Trend in Global Carbon Dioxide Concentrations ........................................ 2

Figure 1.3 Black dots could provide more than the world's total energy demand ................. 3

Figure 1.4 Annual PV Installations ...................................................................................................... 5

Figure 1.5 Efficiency and cost projections for first, second, and third-generation PV

technologies ............................................................................................................................................... 6

Figure 1.6 Best Research-Cell Efficiencies ......................................................................................... 7

Figure 1.7 Band gap energies of the InGaN alloy system cover the entire air-mass-1.5 solar

spectrum ...................................................................................................................................................... 9

Figure 1.8 Schottky InGaN-GaN Solar Cell Structure .................................................................. 13

Figure 2.1 Band diagram of an unbiased p-n junction solar cell (a) in the dark (b) under

illumination ...............................................................................................................................................16

Figure 2.2 Equivalent circuit of a non-ideal solar cell ................................................................... 17

Figure 2.3 Current voltage characteristic of an ideal cell ........................................................... 19

Figure 2.4 Quantum Efficiency of a sample solar cell .................................................................. 20

Figure 2.5 Energy band diagram of Schottky Barrier Solar Cell under illumination .......... 23

Figure 2.6 InGaN-GaN p-i-n junction solar cell structure ......................................................... 24

Figure 2.7 Band Diagram of metal-semiconductor contact ........................................................ 26

Figure 3.1 Cross-sectional schematic of a representational TLM test pattern ..................... 30

Figure 3.2 Planar view of fabricated TLM patterns ...................................................................... 30

Figure 3.3 Four-point measurement system for TLM measurements ...................................... 31

Figure 3.4 Resistance versus Contact Separation ......................................................................... 32

ix

Figure 3.5 I-V Measurements between metal contacts as a function of the distance

between them for 10nm Pt sample ..................................................................................................... 35

Figure 3.6 Total Resistance versus distance between the contacts for 10 nm Pt sample .. 36

Figure 3.7 Total Resistance versus distance between the contacts for 7 nm Pt sample .... 37

Figure 3.8 Total Resistance versus distance between the contacts for 13 nm Pt sample .. 38

Figure 3.9 Sheet resistance as a function of Pt thickness ............................................................ 38

Figure 3.10 Transmission Spectra for 7 nm, 10 nm and 13 nm Pt films ....................................40

Figure 4.1 InGaN/GaN layer structure. ............................................................................................ 42

Figure 4.2 Cross-section of grid style InGaN solar cell ............................................................... 43

Figure 4.3 (a) Coarse Grid (b) Fine Grid ....................................................................................... 44

Figure 4.4 Cross-section of finger style InGaN solar cell .......................................................... 44

Figure 4.5 (a) Coarse Finger (b) Fine Finger ................................................................................. 45

Figure 4.6 Schematic GaN Schottky Solar Cell ............................................................................. 46

Figure 4.7 Short-circuit current per unit length vs Pt Thickness ............................................ 47

Figure 4.8 Short-circuit current density vs Pt Thickness ........................................................... 48

Figure 4.9 Short-circuit current density vs Pt Thickness (zoomed in) .................................. 49

Figure 4.10 Open-circuit voltage vs Pt Thickness ......................................................................... 50

Figure 4.11 I-V curves of a solar cell in the dark ............................................................................. 52

Figure 4.12 I-V curves for the same solar cell under illumination ............................................ 52

Figure 4.13 I-V curves of solar cells under dark and illuminated conditions ........................ 53

Figure 4.14 I-V curves for different InGaN/GaN-Pt solar cell devices under 395 nm LED

illumination .............................................................................................................................................. 54

Figure 4.15 I-V curves for different InGaN/GaN-Pt solar cell devices under 355 nm LED

illumination .............................................................................................................................................. 55

x

Figure 4.16 I-V curves of InGaN/GaN-Pt coarse grid solar cell devices under 395 nm LED

illumination .............................................................................................................................................. 57

Figure 4.17 I-V curves of InGaN/GaN-Pt fine grid solar cell devices under 395 nm LED

illumination .............................................................................................................................................. 57

Figure 4.18 I-V curves of InGaN/GaN-Pt coarse finger solar cell devices under 395 nm LED

illumination .............................................................................................................................................. 58

Figure 4.19 I-V curves of InGaN/GaN-Pt fine finger solar cell devices under 395 nm LED

illumination .............................................................................................................................................. 58

Figure 4.20 I-V curves of InGaN/GaN-Pt (10 nm) solar cell devices under 395 nm LED

illumination .............................................................................................................................................. 59

Figure 4.21 I-V curves of InGaN/GaN-Pt solar cell devices under AM 1.5 illumination .....61

Figure 4.22 J-V curves of InGaN/GaN-Pt coarse grid solar cell devices under 395 nm LED

illumination .............................................................................................................................................. 62

Figure 4.23 J-V curves of InGaN/GaN-Pt fine grid solar cell devices under 395 nm LED

illumination .............................................................................................................................................. 62

Figure 4.24 J-V curves of InGaN/GaN-Pt coarse finger solar cell devices under 395 nm LED

illumination .............................................................................................................................................. 63

Figure 4.25 J-V curves of InGaN/GaN-Pt fine finger solar cell devices under 395 nm LED

illumination .............................................................................................................................................. 63

Figure 4.26 J-V curve of InGaN/GaN-Pt (10 nm) solar cell devices under 395 nm LED

illumination .............................................................................................................................................. 64

Figure 4.27 J-V curves of InGaN/GaN-Pt solar cell devices under AM 1.5 illumination ... 65

Figure 4.28 Short circuit current density as a function of Pt thickness ................................. 66

Figure 4.29 Open-circuit voltage as a function of Pt thickness ................................................ 67

xi

Figure A.1 I-V Measurement Apparatus Setup .............................................................................. 72

xii

List of Tables

Table 1.1 Values of band gap and efficiency for tandems with three to eight junctions

calculated at 500X with a black body spectrum at 6000K .......................................................... 8

Table 3.1 F10-RTA-UVX Specifications ........................................................................................... 34

Table 3.2 Parameter Extraction of Contact Resistance, Sheet Resistance and Transfer

Length ........................................................................................................................................................ 36

Table 3.3 Resistivity of different thicknesses of Pt films ............................................................ 39

Table 4.1 Average short-circuit current and open circuit voltage values along with

standard deviation .................................................................................................................................. 56

Table 4.2 Key differences in finger and grid patterns .................................................................. 60

1

Chapter 1. Introduction

1.1 Harnessing the power of the sun

According to the International Energy Outlook 2013 report, world energy consumption

will increase by 56 percent between 2010 and 2040 [1]. Total world energy use will rise

from 524 quadrillion British thermal units (Btu) in 2010 to 820 quadrillion Btu in 2040, as

shown in Figure 1.1 [1]. At present, we are dependent on non-renewable sources of energy

like coal, petroleum and natural gas for most of our energy needs. However, use of these

conventional energy sources is believed to be the root cause of global warming and thus,

climate change. Climate change is one of the biggest environmental challenges that the

world is facing today. The need of the hour is to consider ways of reducing our carbon

footprint by sourcing our energy needs from renewable energy sources. Global atmospheric

concentrations of greenhouse gases which are responsible for global warming have

increased alarmingly in the past few years. The Keeling curve shown in Figure 1.2 is an

indication of the man-made increases of greenhouse gases (specifically carbon-dioxide)

that contribute towards global warming [2]. Our dependence on non-renewable sources of

energy has increased so much that it also poses the question of how well we would cope in

their absence. Hence, this is the correct time to start looking for alternative energy sources.

While we look for alternative solutions, one of them can be found directly above us, the

Sun!

Solar illumination offers a clean and inexhaustible source of energy. Electric power can be

harnessed from the sun either through thermal or photovoltaic means.

2

Figure 1.1 World Energy Consumption (1990-2040), U. S. E. I. Administration,

"International Energy Outlook 2013," ed, 2013. Used under fair use, 2014.

Figure 1.2 Recent Trend in Global Carbon Dioxide Concentrations, N. O. A.

Administration, "Trends in Atmospheric Carbon Dioxide," ed, 2014. Used under fair use,

2014.

3

Solar energy has by far the highest potential of all the renewable sources of energy. The

sun provides an average of 89,000 terawatts to the earth’s surface. The black dots shown

in Figure 1.3 represent locations that could provide for more than the world’s electricity

demand, if dedicated to solar energy harvesting [3]. Therefore, efficient systems that

harness the sun’s energy must be designed and implemented. Solar cells convert the sun’s

light directly into electricity via the photovoltaic effect. The setup is easy to install; and the

process is highly reliable with low operation and low maintenance costs. It can be a stand-

alone system or it could be integrated with storage systems or connected to the grid. More

importantly, this process is environmental friendly. Therefore, development of highly

efficient, low cost solar cells is an important topic that needs to be studied.

Figure 1.3 Black dots could provide more than the world's total energy demand, M.

Loster, "Total Primary Energy Supply— From Sunlight," ed, 2010. Used under fair use,

2014.

1.2 Brief History and State of the Art of Solar Cells

Solar cells convert sunlight directly into electrical energy using the concept of photovoltaic

effect which was discovered by French physicist Edmond Becquerel in 1839 [4]. When

4

light consisting of photons strike a semiconductor surface, some of them are absorbed by

the electrons in the valence band, which are then excited into the conduction band leaving

behind a hole. In a typical photovoltaic device, due to the built-in electric field, these

excited electrons and holes are pulled away and collected before they can relax. The first

ever large area solar cell was demonstrated by Charles Fritts in 1883 by putting a layer of

selenium between gold and another metal [5]. Significant progress in the field of

photovoltaic devices began in the early 1960s because of the boost that it received from

the space industry owing to the need for power generation on satellites. It was around the

same time that researchers started working on silicon electronics, based largely on the

concept of silicon p-n junctions. The first silicon solar cell demonstrated at Bell

Laboratories had a efficiency of 6% with an estimated cost of $200 per Watt [6]. The

obvious application at the time was space where the cost of the cell was unimportant.

However, the oil crisis of 1973 experienced by the oil dependent western countries led to

renewed focus on photovoltaics for applications other than the space industry. As a result,

photovoltaics started becoming competitive in markets where conventional electricity was

expensive, for example, remote locations or rural places in developing countries. The

potential of solar cells for terrestrial power generation was quickly recognized and this

prompted substantial development of the photovoltaic industry.

During the 1980s, solar cell efficiencies began to increase. In 1985, silicon solar cells

achieved the milestone of 20% efficiency [7]. Solar cell production increased by 15-30%

per annum over the next decade bringing the cost down primarily due to economies of

scale. In recent years, further advancements have brought the cost down to almost $1 per

5

Watt, making terrestrial use of solar cells more feasible. Moreover, novel photovoltaic

materials and device architectures have attracted the attention of many researchers.

The holy grail of solar cell research is the achievement of both high power conversion

efficiency and low-cost in the same device technology. Most common materials used for

solar cell applications are first generation photovoltaics (crystalline and polycrystalline

silicon) and second generation photovoltaics (thin film solar cells like GaAs, CdTe, CIGS).

Multijunction (MJ) solar-cells which form part of the third-generation photovoltaics offer

high efficiencies compared with traditional single junction solar cells. Recently, organic

solar cells have received much attention. A comprehensive review of the current state of

PV technologies has been compiled by Miles et al [8].

Figure 1.4 Annual PV Installations, Solar Energy Market Growth. Available:

http://www.solarbuzz.com/facts-and-figures/markets-growth/market-growth. Used under

fair use, 2014.

6

PV Technology has grown at a remarkable rate over last few decades. The world’s

cumulative PV capacity surpassed the impressive 100-gigawatt (GW) installed electrical

power mark, achieving just over 102 GW in the year 2012 [9]. Annual PV installations has

increased from a little less than 2 GW in 2006 to almost 12 GW in 2010 as shown in Figure

1.4 [10]. The photovoltaic solar industry generated $38.5 billion in revenues in the year

2009; and the solar electric energy demand has grown by 30% per annum in the past two

decades [10]. Despite the rapid rate of growth, the current global PV market is less than

1% of the world energy usage. One of the primary reasons for this small share in the world

energy market can be attributed to high price of solar-generated electricity compared to

other energy sources.

Figure 1.5 Efficiency and cost projections for first, second, and third-generation PV

technologies, M. A. Green, Third Generation Photovoltaics: Advanced Solar Electricity

Generation,” Berlin: Springer-Verlag, 2003. Used under fair use, 2014.

In order for photovoltaics to become economically viable, PV devices must achieve higher

conversion efficiencies while maintaining low costs of production and installation. This

7

leads to the concept of “third-generation” PV having efficiencies greater than single

junction solar cells, while retaining the low cost of second generation photovoltaics. The

goal of third-generation PV is to achieve cost efficiency better than the $1/W target as

shown in Figure 1.5, which is equivalent to the price of fossil-based electricity [11].

Figure 1.6 Best Research-Cell Efficiencies, Best Research Cell Efficiencies. Available:

http://www.nrel.gov/ncpv/. Used under fair use, 2014.

The best research-grade solar cell power conversion efficiencies are summarized in Figure

1.6 [12]. The highest confirmed terrestrial efficiencies measured under AM 1.5 conditions

at 25 degrees are 25% for single-crystal silicon solar cell; and 28.8% for a thin film GaAs

solar cell [13]. Multi-junction solar cells measured under concentrated sunlight are the

dominant technology in terms of conversion efficiency. The current efficiency record is

held by Sharp Corporation. The efficiency of their concentrator-triple junction solar cell

(InGaP top, GaAs middle, and InGaAs bottom) is 44.4% [12]. However, performance of

8

such multi-junction solar cell are slowly reaching their thermodynamic limits for power

conversion efficiencies.

In order to overcome the 50% conversion efficiency barrier, new materials must be

explored. The Indium Gallium Nitride (InGaN) semiconductor alloy offers the potential to

develop ultra-high efficiency solar cells. The advantages and limitations of this material

system are discussed in the following section.

1.3 Indium Gallium Nitride Solar Cell

1.3.1 InGaN Material System

n Values of Band Gap (eV) Efficiency (%)

3 0.7, 1.32, 2 56.0

4 0.60, 1.11, 1.69, 2.48 62.0

5 0.53, 0.95, 1.40, 1.93, 2.68 65.0

6 0.47, 0.84, 1.24, 1.66, 2.18, 2.93 67.3

7 0.47, 0.82, 1.19, 1.56, 2.0, 2.5, 3.21 68.9

8 0.44, 0.78, 1.09, 1.4, 1.74, 2.14, 2.65, 3.35 70.2

Table 1.1 Values of band gap and efficiency for tandems with three to eight junctions

calculated at 500X with a black body spectrum at 6000K, W. Shockley and H. J. Queisser,

"Detailed Balance Limit of Efficiency of p‐n Junction Solar Cells," Journal of Applied

Physics, vol. 32, pp. 510-519, 1961. Used under fair use, 2014.

One of the key requirements to achieve conversion efficiencies greater than 50% is the

need for a material with band gap greater than 2.4 eV [14]. Optimum values for band gaps

of multi-junction solar cells calculated using the detailed balance modeling are presented

in Table 1.1 [15, 16]. The maximum reported conversion efficiency of 44.4% is achieved

9

by a InGaP-GaAs-InGaAs multi-junction solar cell [12]. According to Table 1.1, the

highest theoretical efficiency of a triple junction solar cell is 56%. However, it is observed

that mature PV technologies are typically able to achieve about 80% efficiencies of their

thermodynamic limit [17]. Hence, to achieve conversion efficiencies greater than 50% in

practice, multi-junction solar cells having four or more band gaps may be required.

Therefore, the need for material systems that have band gaps greater than 2.4 eV arises as

evident from the data shown in Table 1.1. With the revision of the band gap of InN from

1.9 eV to 0.7 eV [18, 19], the InGaN system now covers an unusually wide energy range

(0.7 eV to 3.4 eV) relative to the solar spectrum as shown in Figure 1.7 [20]. This suggests

the possibility of multi-junction solar cells using InGaN alloys with a continuum of band

gaps that can be obtained by changing just the Indium composition.

Figure 1.7 Band gap energies of the InGaN alloy system cover the entire air-mass-1.5 solar

spectrum, J. Wu, W. Walukiewicz, K. M. Yu, W. Shan, J. W. Ager, E. E. Haller, et al.,

"Superior radiation resistance of In[sub 1−x]Ga[sub x]N alloys: Full-solar-spectrum

photovoltaic material system," Journal of Applied Physics, vol. 94, p. 6477, 2003. Used

under fair use, 2014.

10

InGaN has been widely used for various optoelectronic devices including laser diodes and

light-emitting diodes [21-24]. InGaN has high potential for solar cell applications due to

superior optical properties [25, 26]. InGaN is a direct band gap semiconductor which means

that the creation of electron hole pairs does not require participation of crystal lattice

vibrations which wastes energy [27]. InGaN also has a high absorption coefficient, on the

order of 105 cm-1 especially in the near band-gap region [28]. This would result in the

absorption of 99% of all incident photons within the first 500nm of InGaN film which

would mean that the cost of the material can be minimized by the use of thin films [29].

Two unique features of InGaN are the presence of large piezoelectric and spontaneous

polarization effects. InGaN has highly polar molecules which results in the development

of electric fields knows as spontaneous polarization. On the other hand, piezoelectric fields

are introduced due to lattice mismatch. Bernardini and Fiorentini have shown that InGaN

has an apparent insensitivity to high dislocation densities because piezoelectric and

polarization effects introduce fields that counter the effect of dislocations [30, 31].

Apart from the above mentioned properties, InGaN also has additional benefits like high

electron mobility [32], high peak and saturation velocities and superior radiation tolerance

compared to other III-V semiconductors [20]. Also, InGaN solar cells do not contain toxic

elements like cadmium, arsenic or phosphorous which are present in other PV technologies

being currently used. These potential advantages are driving immense scientific interest in

this material system.

1.3.2 Research Progress in InGaN Solar Cells

11

As explained earlier, the InGaN material system is a promising candidate for developing

high-efficiency PV systems. Research involving InGaN photovoltaic devices is still in its

initial stages. Since the first proposal in 2003 to use InGaN for solar cell applications,

substantial efforts have already been made in this research space [16]. The first device

showing PV response was reported in 2007 [29]. With a surging interest in InGaN solar

cells, a diverse collection of device structures have been grown and fabricated by various

groups. These include p-i-n homo-junction cells [33, 34], p-i-n hetero-junction cells [29,

35-42], InGaN/Si hetero-junction cell [43, 44], InGaN quantum well solar cells [45, 46]

and InGaN superlattice cells [47]. However, a variety of challenges associated with this

material system (which will be discussed in the next section) have limited the best

conversion efficiencies to around 3-4%. A comprehensive review of the current state of the

art InGaN based PV devices has been compiled by Bhuiyan et al [48]. The following

section will summarize the difficulties and challenges that are limiting the performance of

current InGaN based solar cells.

1.3.3 Challenges with InGaN Solar Cells

The InGaN material system is still in the exploratory and developing stages; and therefore,

there are a lot of challenges that need to be addressed regarding this material system. The

problems can be subdivided in two categories: material based issues and device based

issues. The issues associated with material quality include the following: (1) achieving p-

type conductivity in InGaN alloys, (2) high dislocation density, (3) phase separation and

(4) large lattice mismatch with currently used substrates. The issues related to device

design include: (5) making ohmic contacts to p-type InGaN (or GaN) and (6) searching for

a suitable transparent current spreading layer. While, some progress has been made towards

12

addressing these shortcomings, a number of challenges still exist. The present work will

focus on issue (6) by introducing a novel Schottky structure consisting of a semi-

transparent metal layer (also known as the transparent conductive film) combined with a

semiconductor absorber region.

1.4 Research Objectives

A number of groups have recently investigated InGaN-based homo-junction and hetero-

junction p-i-n solar cells. However, very few groups have worked on InGaN Schottky solar

cells [49, 50]. Compared to p-n junctions, Schottky barrier solar cells are cheaper to grow

and fabricate; they are also expected to improve the spectral response because of near

surface depletion regions in the shorter wavelength regions. Moreover, the difficulty of

growing good quality p-type InGaN has been well documented in literature. Recent efforts

to grow p-type InGaN films have resulted in highly resistive films with current crowding

effects [51, 52]. A transparent conducting layer is, therefore, necessary for InGaN p-n

junction solar cells in order to offset the large resistance of the p-type film. Transparent

conducting layers which are usually semitransparent ultra-thin metal films or metallic

oxides also known as transparent conducting oxides (TCO) are typically placed in direct

contact with the p-side of p-n junction devices and thus must exhibit ohmic behavior with

low contact resistance to such materials. These transparent conducting films are combined

with an opaque contact grid/finger pattern (covering less than or equal to thirty percent of

the surface area) in order to further reduce series resistance. A semi-transparent oxidized

layer of Ni-Au has been widely reported in literature as a current spreading layer for InGaN

p-n junction solar cells.

13

Figure 1.8 Schottky InGaN-GaN Solar Cell Structure

In the present work, the issue of poor quality p-type InGaN was circumvented by using a

Schottky barrier instead of a p-n junction to extract photo-generated carriers. The Schottky

diode structure is shown in Figure 1.8. For the devices considered herein, the transparent

conductive film is one side of the Schottky diode structure as can be seen in Figure 1.8.

There is a clear trade-off between the amount of incident light transmitted through this

transparent conductive film into the cell and the fraction of photo-generated carriers that

are extracted by it. In this study, platinum (Pt) is used to form a Schottky contact with n-

type InGaN/GaN absorber layers which also serves as the transparent conductive film. Pt

is used as the transparent conductive film because it is a well understood metal and it forms

a Schottky barrier with n-type GaN with good rectifying characteristics. Results derived

from this work with Pt will be useful in improving the understanding of InGaN Schottky

solar cells and how this transparent conductive film affects device performance. This work

will also serve as a reference for InGaN Schottky solar cells fabricated with other types of

14

transparent conductive films. In this study, electrical and optical properties of platinum

films of varying thicknesses are investigated. We also report the photovoltaic properties of

InGaN/GaN Schottky solar cell with platinum as the transparent conductive film. The

relationship is studied as a function of the thickness of the metal. Different contact schemes

are employed (layer and grid contacts). An effort is made to explain the impact of these

contact schemes on solar cell performance.

1.5 Organization of Thesis

In Chapter 2, the physics of solar cells with a particular focus on the theory of Schottky

solar cells is discussed at length. The theory of metal semiconductor contacts and concepts

of optical transmission and absorption for semiconductors as well as for thin metal films

are discussed. Chapter 3 describes characterization methods and parameter extraction

techniques used to evaluate the electrical and optical properties of thin metal films. It also

presents a summary of the results. In Chapter 4, solar cell characterization techniques and

our results are presented. Chapter 5 concludes the thesis, the results are summarized and

the scope of this research is presented.

15

Chapter 2. Schottky Barrier Solar Cells: Principles of Operation

2.1 Theory of P-N Junction Solar Cells

A solar cell is a device which converts sunlight into electricity. The cell is a two terminal

device that behaves like a diode in the dark and generates a photocurrent in the presence of

light. The basic principle behind its operation is the photovoltaic effect. When light made

of packets of energy, called photons strike the surface of the cell, photons with energies

greater than the band-gap, 𝐸𝑔, of the absorbing material get absorbed while the photons

with energies less than 𝐸𝑔 pass through the material. Each photon absorbed by the solar

cell, excites an electron from the valence band to conduction band, thus creating an

electron-hole pair. Electrons generated in the p-type material and holes in the n-type

material are “minority carriers” and thus will only exist for a duration of time equal to the

minority carrier lifetime before they recombine. If recombination occurs, then no electrical

power will be generated. Instead the goal is to have these minority carriers diffuse through

the quasi-neutral regions until they reach the p-n junction as shown in Figure 2.1. The

minority carriers are then swept across the p-n junction by the action of the electric field

existing across the depletion region. The electrons move towards n-side, while the holes

move towards the p-side. Once the photo-generated electrons (holes) reach the n-side (p-

side) of the junction they contribute to the majority carrier currents in these regions. In

essence, photovoltaic action results from three steps which are charge generation (photons

generating electron-hole pairs), charge separation, and charge transport. Due to the

presence of these excess carriers, a voltage is set up across the junction which splits the

equilibrium Fermi-level into two quasi-Fermi levels, one for electrons (𝐸𝑓,𝑛) and the other

16

for holes (𝐸𝑓,𝑝) shown in Figure 2.1. When the contacts to the cell are isolated, the potential

difference across the diode has its maximum value which is equal to the open-circuit

voltage (𝑉𝑜𝑐). If the solar cell is short-circuited, the current density that flows is known as

the short-circuit current density (𝐽𝑠𝑐).

Figure 2.1 Band diagram of an unbiased p-n junction solar cell (a) in the dark (b) under

illumination

The net current density delivered, J, by a solar cell to a resistive load is:

J(V) = Jsc − Jdark(V) (2.1)

where Jdark is the dark current density. For a non-ideal diode, Jdark is given by:

J𝑑𝑎𝑟𝑘(V) = J0(eqV nkBT⁄ − 1) (2.2)

17

Thus, 𝐽 becomes:

𝐽(V) = Jsc − J0(eqV nkBT⁄ − 1) (2.3)

where V is the voltage across the diode, 𝐽0 is the saturation current density, n is the ideality

factor of the diode, 𝑘𝐵is the Boltzmann constant and T is the temperature. The “open-

circuit” condition is defined by 𝐽(𝑉𝑜𝑐) = 0 and therefore we can rearrange Equation 2.3

to find Voc, which is given by:

Voc =

nkT

qln (

Jsc

J0+ 1) (2.4)

Equation 2.4 shows the relationship between open-circuit voltage and the short circuit

current. The open circuit voltage can also be thought of as the difference between the quasi-

Fermi levels across the p-n junction, and thus, it is limited by the band gap of the

semiconductor as show in Figure 2.1.

Figure 2.2 Equivalent circuit of a non-ideal solar cell

18

Such an ideal solar cell can be represented by a current source in parallel with a diode. A

more realistic equivalent circuit model, including series and shunt resistances is shown in

Figure 2.2 [7]. The net current density taking into account the series and shunt resistance

is given by the following equation:

J = Jsc − J0 (e

(q(V−J.Rseries)

nkT)

− 1) +V − J. Rseries

Rshunt (2.5)

where Rseries and Rshunt represent specific resistances with 𝛺𝑐𝑚2 as their units. In non-

ideal solar cells, power is dissipated through the series and shunt resistances included in

equation 2.5. The total series resistance has contributions from the bulk semiconductor

material, the contact resistance associated with the semiconductor/metal interface and the

resistance of the front and rear metal electrodes. Shunt resistance arises primarily from

electrically active defects introduced either during materials synthesis or device

fabrication. Both series and shunt resistances have a detrimental impact on the fill factor

(explained in the next paragraph) and hence, the overall efficiency of a solar cell. The

power density delivered by a solar cell to a resistive load is given by:

P = J. V (2.6)

The open-circuit voltage (I = 0) and short-circuit (V = 0) current are labeled on the

prototype solar cell J-V curve shown in Figure 2.3. However, no power is generated at

these two points. The power density in a solar cell reaches its maximum value at some

voltage 𝑉𝑚with a corresponding current density of 𝐽𝑚. The maximum power is calculated

by setting the derivative of power density equal with respect to voltage to zero.

𝑑𝑃

𝑑𝑉= 0 (2.7)

19

The fill factor is an important parameter that determines the maximum power that can be

drawn from a solar cell. The fill factor is defined as the ratio:

FF =

Jm. Vm

Jsc. Voc (2.8)

Figure 2.3 Current voltage characteristic of an ideal cell

Graphically, the fill factor describes the ‘squareness’ of the J-V plot in the sense that with

Vm = Voc and Jm = Jsc, the J-V curve would outline a rectangle and FF = 1. It also

represents the largest rectangle that can be inscribed inside the J-V curve shown in Figure

2.3. The efficiency ƞ of a solar cell is defined as the ratio of the maximum power density

delivered to the load and the incident light power density, 𝑃𝑖𝑛𝑐:

ƞ =

Jm. Vm

Pinc=

Jsc. Voc. FF

Pinc (2.9)

These quantities 𝐽𝑠𝑐, 𝑉𝑜𝑐 , 𝐹𝐹 and ƞ are the essential “device metrics” of a solar cell. In order

to make useful comparisons of solar cell performance, these parameters should be

Cu

rren

t D

ensi

ty, J

Voltage, V

Maximum power point

Jsc

Jm

VocVm

20

measured under “standard” illumination conditions. The standard spectrum at the Earth’s

surface is AM1.5G (the G stands for global and includes both direct and diffuse radiation)

or AM1.5D (which includes direct radiation only) [7]. The standard spectrum outside the

earth’s atmosphere is AM0 (air mass zero).

Quantum efficiency is an important diagnostic quantity in that its spectral dependence can

be used to identify shortcomings in material quality and/or layer structure design. The

external quantum efficiency (EQE) of a solar cell is the ratio of the number of carriers

flowing through the electrical circuit to the number of photons incident on the solar cell.

The internal quantum efficiency (IQE) of a solar cell is obtained from the EQE by including

only absorbed photons (i.e. by subtracting out photons lost to reflection or transmission

from the incident light intensity). A sample quantum efficiency curve is shown in Figure

2.4. As seen in Figure 2.4, the quantum efficiency is reduced due to recombination effects.

It is also affected by short diffusion lengths and reflections occurring at the top surface.

Figure 2.4 Quantum Efficiency of a sample solar cell

21

The impact of carrier recombination on solar cell performance is represented by two

quantities which are minority carrier lifetime and diffusion length. Minority carrier lifetime

(𝜏) is the average time which a photo-generated carrier spends in an excited state before it

recombines.

1

τ=

1

τradiative+

1

τauger+

1

τSRH (2.10)

where 𝜏𝑟𝑎𝑑𝑖𝑎𝑡𝑖𝑣𝑒 , 𝜏𝑎𝑢𝑔𝑒𝑟 and 𝜏𝑆𝑅𝐻 represent minority carrier lifetimes as a result of

radiative, Auger and Shockley-Read-Hall recombination mechanisms [5]. In the radiative

process, an electron from the conduction band recombines with a hole in the valence band

and releases a photon. Recombination through point defects occurs via the Shockley-Read-

Hall mechanism which is a two-step process. An electron is trapped by an energy state

within the band-gap which is due to defects present in the crystal lattice. If a hole moves

up to the same energy state before the electron is re-emitted, then the electron and hole

recombine. In Auger recombination, three particles are involved. First, the electron

recombines with a hole to give out energy which is then given to an electron in the

conduction band (hole in the valence band) pushing it high into the conduction (valence)

band. The excited electron (hole) gradually loses that energy thermally to come back to the

edge of the conduction (valence) band.

Diffusion length (L) is the average distance a carrier diffuses in a concentration gradient

from the point of generation until it recombines.

L = √Dτ (2.11)

where D is the diffusion coefficient and can be found using

22

D = μ

kT

q (2.12)

The value of τ depends on the number of defects in the bulk material via the SRH term in

Equation 2.10. Also, since the surface of a solar cell presents a disruption of the lattice, the

surface is a site of particularly high recombination. Surface recombination velocity is the

parameter which is used to quantify recombination at the surface. The recombination of

charge carriers has a major impact on the open circuit voltage of the solar cell. High

recombination increases the forward-bias recombination current of the diode, which in turn

decreases the open circuit voltage of the solar cell. It can be seen how parameters like

diffusion length and surface recombination affect the quantum efficiency of a solar cell in

Figure 2.4.

2.2 Theory of Schottky Barrier Solar Cells

The energy band diagram for a Schottky barrier (metal/n-semiconductor) solar cell is

shown in Figure 2.5. The metal is deposited as a semi-transparent film through which most

of the light can pass. Light transmitted through the metal into the semiconductor is

absorbed to generate photocurrent. A very small part of the photocurrent is also contributed

by light absorption in the thin metal layer (although this photocurrent is negligible and is

not considered in the analysis). The current density versus voltage characteristic of a

Schottky barrier solar cell under illumination is similar to Equation 2.3 for the p-n junction,

which is restated here:

J = Jsc − J0(eqV nkBT⁄ − 1) (2.13)

where 𝐽0, the saturation current density, is now given by:

23

J0 = A∗∗. T2. exp(−q. φb kb. T⁄ ) (2.14)

where 𝐴∗∗ is known as the Richardson constant and 𝜑𝑏is the Schottky barrier height.

Figure 2.5 Energy band diagram of Schottky Barrier Solar Cell under illumination

The metal-semiconductor junction (Schottky diode) is a simple way to prepare a

photovoltaic device. The other main advantage of a Schottky barrier solar cell is the

presence of the depletion region right next to the metal surface which reduces the surface

recombination probability and thus, improves the spectral response for high energy

photons. However, Schottky barrier solar cells have a few limitations. A Schottky barrier

solar cell cannot produce high open circuit voltages because the maximum value is limited

by the potential energy difference between the metal work function and semiconductor

electron affinity. Whereas, for a p-n junction solar cell, the open circuit voltage can be

roughly x% of the semiconductor band-gap. Secondly, in the case of highly doped

semiconductors, thin barrier layers may result in tunneling of carriers which will reduce

24

the photocurrent. Moreover, the material interface between the semiconductor and metal

contains interface states which may trap charge and reduce the open circuit voltage.

2.3 Solar Cells with Transparent Conducting Films

One of the most important design considerations for both Schottky and p-n junction solar

cells is to minimize resistive losses. As explained before, series resistance arises due to

material properties and electrode design. In order to decrease the material resistance,

doping can be increased which also enhances the electric field to help in carrier collection.

However, for a Schottky structure, increased doping may result in tunneling which reduces

the net photocurrent. Electrode resistance is generally reduced by increasing the

dimensions and thickness of metal fingers or grid patterns used as the top electrodes. This,

however, is done at the cost of reducing the transmission of light entering the cell. Careful

optimization of the line-width and grid-spacing is required in order to improve efficiencies.

Figure 2.6 InGaN-GaN p-i-n junction solar cell structure

25

Transparent conducting layers which are usually thin (semitransparent) metal films or

metallic oxides (also known as transparent conducting oxides or TCOs) are used as current

spreading layers between the top metal electrode and the p-side of the p-n junction, as

shown in Figure 2.6. These layers are especially important in InGaN p-n junction solar

cells because of the large resistance associated with p-type GaN films. The current

spreading layer has a strong influence on the performance of InGaN p-n junction solar

cells. In addressing this issue, a semi-transparent oxidized layer of Ni-Au has been widely

reported in literature as a current spreading layer. However, there are very few reports on

the issue of optimizing this layer or looking for other options. A couple of papers have

reported the effect on photovoltaic response by using ITO instead of Ni-Au current

spreading layers [53-55].Neufeld also demonstrated that the performance of InGaN p-n

junction solar cells can be improved by optimizing the metal electrode grid spacing [35].

In the present work, a transparent conductive film has been used to form a Schottky barrier

with the InGaN/GaN absorber region, thus, forming an active part of the solar cell shown

previously in Figure 1.8. Ultra-thin metal films of Pt have been used as the transparent

conductive material. This work will investigate the feasibility of InGaN based Schottky

solar cells with Pt serving as both the Schottky barrier “metal” and the current spreading

layer.

2.4 Metal-Semiconductor Contacts

The energy band diagram of a metal-semiconductor contact at equilibrium is shown in

Figure 2.7. Metal semiconductor contacts form an important part of all semiconductor

26

devices. A metal-semiconductor junction results in either an ohmic contact or Schottky

barrier. In an ohmic contact, there is a linear relationship between current and voltage (for

both voltage polarities) and the goal is to minimize the voltage drop for a desired current

flow. The contact resistance should be as small as possible in comparison to the bulk

resistance of the semiconductor. The current-voltage curve of an “ohmic” contact should

ideally be linear. However, in practice, the current-voltage curve of an ohmic contact does

not have to be exactly linear in order for it to be useful. In a Schottky barrier or rectifying

contact, current is blocked for one polarity of voltage. Thus, the current voltage curve of a

Schottky contact should be rectifying in nature like a diode.

Figure 2.7 Band Diagram of metal-semiconductor contact

The Schottky barrier height of a metal/ n-type semiconductor interface is given by:

q. φB,n = q. (φM − χ) (2.15)

27

where, 𝜑𝐵,𝑛 is the barrier height, 𝜑𝑀is a the work function of metal and χ is the electron

affinity of the semiconductor. For an n-type semiconductor, in order to make an ohmic

contact, the work function of the metal must be smaller than the electron affinity of the

semiconductor. For a p-type semiconductor, the formation of an ohmic contact requires the

work function of the metal to be larger than the sum of the electron affinity and the band

gap energy. Since the maximum value of work function for known metals is just above 5

eV and a typical value of electron affinity is about 4 eV, it is extremely tough to find metals

that form ohmic contacts to p-type semiconductors with wide band gaps such as GaN [56,

57]. Notwithstanding this situation, Ho demonstrated that Ni-Au layers when annealed in

oxygen ambient make ohmic contacts to p-type GaN with specific contact resistances as

low as 10−6𝛺. 𝑐𝑚−2 [58, 59]. It is important to recognize that TCOs that form good ohmic

contacts to p-type GaN and p-type InGaN should yield Schottky barriers to n-type GaN

with large values of φB,n.

2.5 Absorption and Transmission in Thin Films

The process of fundamental or band-to-band absorption refers to photons exciting an

electron transitions from the valence band to the conduction band in a semiconductor (or

lower filled band to higher empty band in a metal or metal oxide film). A bulk

semiconductor’s optical absorption coefficient 𝛼 can be calculated from its optical

transmission data. When light of intensity 𝐼0 is incident on a film of thickness 𝑥, a

transmitted intensity 𝐼 emerges out of the other side. Beer Lambert’s law states that there

is a logarithmic relation between the absorption coefficient and the transmitted optical

intensity according to the following equation:

28

T =

I

𝐼0= e−αx (2.16)

where, 𝛼 is the absorption coefficient at a fixed wavelength. This equation assumes there

is no scattering of light within the semiconductor film. This equation also does not take

into account power reflection/transmission at the top and bottom film surfaces. Accounting

for multiple reflections that occur at the film surfaces, the transmission coefficient 𝑇 =

𝐼/𝐼0 is given by [60]:

T = [(1 − R)2. 𝑒𝑥𝑝 (−α. x)]/[1 − R2. exp(−2. α. x)] (2.17)

where, R is power reflection coefficient at the air-film interface, given by:

R = [(n − 1)2 + k2]/[(n + 1)2 + k2] (2.18)

Note that the equation treats the air/film and air/substrate interface the same. Equations

2.17 and 2.18 are used to calculate the absorption coefficient of thin films using the optical

transmission and reflection data.

TCO materials are not typically used as current spreading layers in III-V multi-junction

solar cells and crystalline silicon solar cells [61, 62]. The reason for not using a TCO in

these solar cells is because they require high transmittance near the infrared region which

none of the current TCOs can provide. Transmission in the infrared region is limited by

free carrier absorption. Free carrier absorption occurs when a material absorbs a photon

and the carrier is excited from a filled state to an unoccupied state within the same band.

In a simple Drude theory formulism, the plasma wavelength, 𝜆𝑝, or the onset of total

reflection can be expressed as [63, 64]:

29

λp = 2πc√ε∞m∗

4πne2 (2.19)

where ε∞ is the high frequency permittivity, n is the free electron concentration and 𝑚∗ of

effective mass of the electron which depends on the energy band structure. For wavelengths

shorter than 𝜆𝑝, transmission is limited by free carrier absorption. The dependence of 𝜆𝑝

on the effective mass, and the connection between effective mass and carrier mobility,

implies that increasing transmission in the IR region requires TCOs with high mobility.

Equation 2.19 also shows that materials with low carrier concentrations are required to

push λp into the UV range where the solar radiation spectrum is relatively weak. However,

lowering the electron concentration reduces the conductivity of a material whereas, high

conductivity is a desired characteristic of a TCO. The same is true for semi-transparent

metals used as transparent conductive layers. Hence, an ideal TCO (or semi-transparent

film) requires optimization of optical transparency and electrical conductivity.

The next two sections of this thesis will focus on characterization methods used for this

work. There are two parts to characterization methods used in this study. The first part

which is summarized in Chapter 3 focusses on the characterization of thin metal films of

Pt which will be used as the transparent conducting layer in our Schottky barrier solar cell.

The second part involves solar cell characterization with Pt films serving as the TCO

electrode which will discussed in Chapter 4.

30

Chapter 3. Characterization of Transparent Conducting Films

This chapter will present the characterization methods and parameter extraction techniques

used to characterize the transparent conducting films which are integral to the Schottky

solar cells of interest here. The measurement results will also be presented.

3.1 Transfer Length Measurements (TLM)

Transfer Length Measurements or Transmission Line Measurements is a technique used to

determine the contact resistance between a metal and a semiconductor originally proposed

by Shockley [65]. However, we will use this technique to calculate the sheet resistance of

our thin metal films. This method requires making a series of metal-semiconductor (or thin

metal film) contacts separated by increasing distances.

Figure 3.1 Cross-sectional schematic of a representational TLM test pattern

Figure 3.2 Planar view of fabricated TLM patterns

31

Figure 3.1 is a cross-sectional schematic of a TLM test pattern. The thin film (with

thickness equal to 𝑡𝐹) under test is deposited on double side polished sapphire. 50nm of

Nickel (Ni) followed by 400nm of Silver (Ag) is used as the ohmic contact layer. Figure

3.2 is an optical image of a fabricated TLM test pattern. The metal contacts are separated

from each other in the following order of distances: 7 𝜇m, 10 𝜇m, 13 𝜇m, 16 𝜇m, 20 𝜇m

and 25 𝜇m.

Figure 3.3 Four-point measurement system for TLM measurements

A four-point measurement configuration is used as shown in Figure 3.3. The probes are

applied to one pair of contacts at a time and then cycled through all the contact pairs in the

structure. I-V measurements were made using a Keithley 2400 source meter which is used

to ramp the current while simultaneously measuring the voltage drop across the contacts.

The resistance measured is a summation of the interfacial metal/film resistance (Rc) of

both contacts plus the sheet resistance (Rsh) of the thin film. Once resistance

measurements are made for all adjacent pairs of contacts, a plot of resistance versus contact

separation can be made which should yield in a straight line. The equation is:

32

RT =

Rsh

W. l + 2. Rc (3.1)

where, 𝑅𝑠ℎ is the sheet resistance, 𝑊 is width of the metal contact, 𝑙 is the distance between

the contacts and 𝑅𝑐 is the contact resistance.

Figure 3.4 Resistance versus Contact Separation

Figure 3.4 is a plot of resistance versus contact separation for representation purposes. The

red triangles denote measurement data points and the dotted black line represents a linear

fit to the data points. The slope and the y intercept of the line are used to extract the sheet

resistance and the contact resistance. The x intercept is equal to twice the transfer length

which can be extrapolated from the equation of the line. The transfer length is the average

distance that an electron (or a hole) travels in the film beneath the contact before it flows

up into the contact. So the effective area of the contact is:

A = LT. W (3.2)

The contact resistance can be defined as:

y = 0.9635x + 18.514R² = 0.9994

0

5

10

15

20

25

30

35

40

45

0 5 10 15 20 25 30

Res

ista

nce

(Ω)

Length (μm)

33

RC =

ρc

LT. W=

Rsh. LT

W (3.3)

While this method is widely used to calculate sheet resistances of thin films and contact

resistances of metal contacts; it also makes a few assumptions that we should be aware of.

The first assumption is that the contact resistance of all metal contacts are identical.

Secondly, the assumption of electrically long contact (𝐿>>𝐿𝑇) enables the relationship

𝜌𝑐 = 𝑅𝑠ℎ. 𝐿𝑇2, used in our analysis. Lastly, we assume that the metal contact does not alter

the sheet resistance of the thin film which might not always be true. Reeves described a

method to calculate the modified sheet resistance and also showed how to deduce specific

contact resistance by carrying out an end resistance measurement [65]. However, we will

not calculate the modified sheet resistance. The TLM method, described above, will be

used herein to determine the sheet resistance of the transparent conductive films (thin Pt

films in this case) employed in the Schottky solar cells. Additional details regarding

measurement setup and calibration procedure can be found in Appendix A.

3.2 Transmission and Reflection Measurements

The two most common techniques for determining film thickness are optical and stylus

based measurements. Optical techniques are preferred because they are more accurate and

non-destructive. The most common optical measurement systems are spectral reflectance

and ellipsometry. Spectral reflectance measures the reflected light from a thin film when

light is normally incident on it over a range of wavelengths. Ellipsometry is similar, except

that it uses non-normal incident light at two different polarizations. The optical properties

of thin films used in this work were studied by using a F10-RTA-UVX Filmetrics

Measurement System. The F10-RTA-UVX reflectometer captures reflectance and

34

transmittance spectra simultaneously across a wide range of wavelengths (200nm-

1700nm). The software converts these spectra into thickness and refractive index data. The

specifications of the F10-RTA-UVX are shown below in Table 3.1.

Specifications F10-RTA-UVX

Wavelength Range 200-1700 nm

Thickness Range 3 nm-150 µm

Minimum Thickness to measure n and k 15 nm

Thickness Accuracy 1 nm

Thickness Precision 0.1 nm

Thickness Stability 0.07 nm

Light Source D2+Halogen

Table 3.1 F10-RTA-UVX Specifications

The Filmetrics measurement system will be used to study the optical characteristics of the

thin Pt films which will be used as transparent conductive films in Schottky solar cells.

Specifically, we will measure the transmission spectra of these Pt films.

3.3 Data Analysis and Discussion

3.3.1 TLM Results

Platinum films of varying target thicknesses (7 nm, 10 nm and 13 nm) were deposited on

double side polished sapphire using electron-beam evaporation with a base pressure lower

than 2 × 10−6 Torr. The thickness of the Pt films were measured using a Zygo surface

profiler to confirm the thickness deposited, which showed a maximum absolute error of 1

nm. TLM patterns were formed as shown in Figure 3.1. The metal film under test was

patterned with Ni (50nm) / Ag (400nm) as the metal contact with interspacings of 7 𝜇m,

10 𝜇m, 13 𝜇m, 16 𝜇m, 20 𝜇m and 25 𝜇m. The TLM patterns were defined by a

photolithographic lift-off process. I-V measurements between pairs of contacts with

35

varying distances on the TLM patterns revealed linear behavior for all the three platinum

films, which was expected.

Figure 3.5 I-V Measurements between metal contacts as a function of the distance

between them for 10nm Pt sample

Figure 3.5 shows the I-V measurements made across pairs of contacts with varying

distances for the sample with a 10 nm thick Pt film. These I-V measurements across pairs

of contacts with varied spacing were used to calculate the associated resistances. As can be

seen in Figure 3.5, the slope of the I-V curves keeps decreasing with increasing distances,

which indicates an increase in the resistance as a function of distance, which is expected.

These resistance values are then plotted as a function of distance in order to extract the

sheet resistance of the Pt film. Figure 3.6 shows the total resistance versus distance curve

for the 10 nm Pt sample for eight different TLM patterns. As can be seen in the figure, all

eight TLM patterns show linear behavior with a positive slope.

-1.5E-03

-1.0E-03

-5.0E-04

0.0E+00

5.0E-04

1.0E-03

1.5E-03

-6.0E-03 -4.0E-03 -2.0E-03 0.0E+00 2.0E-03 4.0E-03 6.0E-03

Cu

rren

t (A

)

Voltage (V)

7um

10um

13um

16um

20um

25um

36

Figure 3.6 Total Resistance versus distance between the contacts for 10 nm Pt sample

The slope and the y-intercept of the straight line fit corresponding to each TLM pattern is

used to calculate the sheet resistance of the Pt film. Table 3.2 shows all the parameters

extracted using the techniques described in Section 3.1.

TLM Pattern # Slope (m)

y-intercept

(m) R2 RC () LT (m) RSH (/sq)

1 0.161 1.333 0.999 0.666 4.133 62.913

2 0.156 1.208 0.998 0.604 3.852 61.196

3 0.140 1.375 0.997 0.687 4.902 54.690

4 0.134 1.527 0.999 0.763 5.686 52.396

5 0.145 1.267 0.999 0.633 4.363 56.650

6 0.150 1.211 0.998 0.605 4.027 58.649

7 0.144 1.282 0.997 0.641 4.432 56.431

8 0.135 1.379 0.999 0.689 5.073 53.032

Table 3.2 Parameter Extraction of Contact Resistance, Sheet Resistance and Transfer

Length

0.0

1.0

2.0

3.0

4.0

5.0

6.0

0 5 10 15 20 25 30 35

Resis

tan

ce ()

Length (m)

TLM Pattern 1

TLM Pattern 2

TLM Pattern 3

TLM Pattern 4

TLM Pattern 5

TLM Pattern 6

TLM Pattern 7

TLM Pattern 8

37

The 𝑅2 value is known as the coefficient of determination which indicates the “goodness”

of a fit for a particular set of data points. Values close to one indicate a very good fit of the

data points. Once, the slope and y-intercept are obtained, all other parameters of interest

can be calculated using the method described earlier. The average sheet resistance of the

10 nm Pt film was calculated to be 57 Ω/sq.

Figure 3.7 shows the total resistance versus distance curve for the 7 nm Pt sample for eight

different TLM patterns. As can be seen in the figure, all eight TLM patterns except for one

pattern (Pattern #2) exhibit linear behavior with a positive slope. The average sheet

resistance of the 7 nm Pt film was calculated to be 103.9 Ω/sq.

Figure 3.7 Total Resistance versus distance between the contacts for 7 nm Pt sample

Figure 3.8 shows the total resistance versus distance curve for the 10 nm Pt sample for

eight different TLM patterns. As can be seen in the figure, all eight TLM patterns except

0.0

2.0

4.0

6.0

8.0

10.0

12.0

0 5 10 15 20 25 30 35

Resis

tan

ce ()

Length (m)

TLM Pattern 1

TLM Pattern 2

TLM Pattern 3

TLM Pattern 4

TLM Pattern 5

TLM Pattern 6

TLM Pattern 7

TLM Pattern 8

38

for one pattern (Pattern #8) show linear behavior with a positive slope. The average sheet

resistance of the 13 nm Pt film was calculated to be 41.5 Ω/sq.

Figure 3.8 Total Resistance versus distance between the contacts for 13 nm Pt sample

Figure 3.9 Sheet resistance as a function of Pt thickness

0.0

1.0

2.0

3.0

4.0

5.0

6.0

7.0

8.0

9.0

0 5 10 15 20 25 30 35

Resis

tan

ce ()

Length (m)

TLM Pattern 1

TLM Pattern 2

TLM Pattern 3

TLM Pattern 4

TLM Pattern 5

TLM Pattern 6

TLM Pattern 7

TLM Pattern 8

0

20

40

60

80

100

120

140

6 7 8 9 10 11 12 13 14

Shee

t R

esis

tan

ce(Ω

)

Thickness (nm)

39

Figure 3.9 shows the average sheet resistance as a function of the thickness of platinum. It

is evident from the figure that the sheet resistance of the Pt films decreases as the thickness

of the Pt film increases, which is expected. The sheet resistance (𝑅𝑆𝐻) and the thickness of

the metal film (𝑡𝐹) can be used to calculate the resistivity (𝜌) of the Pt film using the

following equation.

𝜌 = 𝑅𝑆𝐻. 𝑡𝐹 (3.20)

Table 3.3 shows calculated values of resistivity for the different thicknesses of Pt films.

Thickness of Pt film (nm) Resistivity (Ω.cm)

7 nm 7.28e-5

10 nm 5.69e-5

13 nm 5.39e-5

Table 3.3 Resistivity of different thicknesses of Pt films

It is evident from Table 3.3 that the resistivity of these thin films decreases as the thickness

of the film increases. By definition, it is fair to assume that intrinsic properties of a metal

film such as electrical resistivity should be independent of its thickness. However, this is

not true for ultra-thin metal films. The resistivity of bulk Pt is 1.06e-5 Ω.cm. In the case of

thin film metals, the resistivity is much larger than the resistivity of bulk metal; and it

decreases with increasing thickness of the metal film, until it achieves a value close to the

bulk resistivity. Moreover, the electrical resistivity of the metal film is affected by the film

thickness as soon as the thickness of the film becomes comparable to the electron mean

free path in that medium.

3.3.2 Optical Results

40

Figure 3.10 Transmission Spectra for 7 nm, 10 nm and 13 nm Pt films

Optical transmission measurements were made on Pt films with three different thicknesses

(7 nm, 10 nm and 13 nm). These metal films were deposited in the same e-beam

evaporation runs as the TLM samples described in Section 3.3.1 (but the films were not

patterned). Figure 3.10 shows the raw transmission spectra. No effort has been made to

correct these transmission spectra for reflection losses occurring at the air-Pt and Pt-

Sapphire interfaces. It is evident in Figure 3.10 that the overall transmission as a percentage

decreases as the film thickness increases, which is expected.

3.3.3 Summary of Results

The measurement results shown herein demonstrate the connections between Pt film

thickness, electrical sheet resistance and optical power transmission. While the sheet

10

20

30

40

50

60

70

80

90

200 400 600 800 1000 1200 1400 1600

Tran

smis

sio

n (

%)

Wavelength (nm)

DSP Sapphire

7nm Pt

10nm Pt

13nm Pt

41

resistance of the thin film decreases with increasing thickness, the optical transmission

through the film increases with decreasing film thickness. Consequently, as suggested

before, there is a tradeoff between the optical losses and series resistance for the transparent

conductive films which will serve as key elements of the Schottky solar cells described

next. An ideal transparent conductive film would yield the lowest possible values of optical

loss and series resistance. However, from the results presented here, it is clear that both

these properties cannot be achieved at the same time. Hence, an effective transparent

conductive film needs careful optimization of both the electrical and optical properties in

order to improve the performance of InGaN/GaN Schottky solar cells.

42

Chapter 4. Solar Cell Characterization

It is clear from the previous section that the thickness of the Pt films affect their electrical

and optical properties. When a Pt film is used as a transparent conductive film in a Schottky

solar cell, the optical properties of the Pt film influence the amount of light passing through

it and reaching the absorber layer. On the other hand, the electrical resistivity of the Pt film

impacts the collection of photo-generated carriers. As a result, the material properties of Pt

(in thin-film form) should significantly impact the performance of the solar cell. Now that

we have a better understanding of the Pt films and their properties; the next step is to

understand the impact of film thickness on the photovoltaic properties of InGaN/GaN

Schottky solar cells.

4.1 Solar Cell Structure

Figure 4.1 InGaN/GaN layer structure.

The InGaN/GaN structures were grown on c-plane sapphire substrates by organometallic

vapor phase epitaxy (OMVPE). The layer structure grown is shown in Figure 4.1. The

structure consists of a 4.0 μm thick, Si-doped n-GaN ohmic contact layer (n = 2 ×1018 cm-

3), followed by a nominally un-doped GaInN/GaN absorber capped by a 40 nm thick, un-

43

doped GaN window layer. The absorber consists of a 30-pair MQW region with 2.5 nm

thick GaInN quantum wells and 12 nm thick GaN barriers. The indium content in the

InGaN quantum wells is about 10%. Mesa fabrication was performed using an inductively

coupled plasma (ICP) etching system to isolate devices from each other and also to expose

the n-GaN ohmic contact layer. Pt is used as the transparent conducting film which also

serves as a large-area Schottky contact to the un-doped GaN window layer. The Schottky

metal films were deposited by electron-beam evaporation. Two distinct geometries, each

having two different values of metal line pitch, are used as the top electrode. The first kind

of geometry used is grid style geometry shown in Figure 4.2. The top-side metal traces are

made of a Ni (50 nm) / Ag (400 nm) bilayer and have a line width of 5 µm.

Figure 4.2 Cross-section of grid style InGaN solar cell

The device structure has a square-shaped mesa surrounded by another metal trace that

serves as the bottom-side electrode. A Ti/Al (30nm/400nm) composite, deposited using

electron beam evaporation, was used as the ohmic contact to n-type GaN. Figure 4.3 shows

44

Nomarski optical images of fabricated solar cells with two different grid spacings (75 µm

and 150 µm). The two contact patterns are referred to in the following discussion as coarse

grid and fine grid.

Figure 4.3 (a) Coarse Grid (b) Fine Grid

Figure 4.4 Cross-section of finger style InGaN solar cell

45

Figure 4.5 (a) Coarse Finger (b) Fine Finger

The second kind of electrode geometry used is a finger style geometry as shown in Figure

4.4. In this case, the mesa has an interleaved comb-like structure with the layer structure

removed to make ohmic contact traces adjacent to each mesa finger. Figure 4.5 shows

fabricated solar cells with two different metal trace pitches (75 µm and 150 µm). These

two contact patterns are referred to in the following discussion as coarse finger and fine

finger.

Three different solar cells were fabricated using the same GaN/InGaN layer structure, each

having the four different electrode geometries described above. Each solar cell had a

different thickness of Pt, the thicknesses being 7 nm, 10 nm and 13 nm. The size of an

entire solar cell device (including the non-mesa area) is 1.4 x 1.4 mm2, and there is no anti-

reflection coating for all four geometries.

46

4.2 Crosslight APSYS Simulation

Crosslight APSYS is a general-purpose software that uses the finite element method to

simulate the performance of semiconductor devices. The program solves several equations

simultaneously including the basic Poisson’s equation and drift-diffusion current

equations. Modelling InGaN based solar cells presents several challenges, the most

important of which are uncertainty in key material parameters and proper implementation

of spontaneous polarization and piezoelectric effects. Hence, in this work, GaN Schottky

solar cells are investigated in order to avert these issues.

Figure 4.6 Schematic GaN Schottky Solar Cell

Simulations were used to study the impact of Pt layer thickness on short-circuit current

density and open-circuit voltage of the solar cell. Only the coarse finger and fine finger

geometries were used for simulation purposes. All physical dimensions used in the

simulations match the actual solar cell devices in an effort to accurately model the 2D

effects. Figure 4.6 shows the schematic of the GaN solar cell simulated using Crosslight.

The structure consists of a 2.0 μm thick n+ GaN ohmic contact layer (n = 1 ×1018 cm-3),

followed by a 0.5 μm thick n-type GaN (n = 1 ×1016 cm-3) absorber layer. The thickness of

the n-type GaN layer is equal to the thickness of the active region part of InGaN/GaN layer

47

structure. However, the thickness of the n+ GaN ohmic contact layer is 2 μm thinner than

that of corresponding layer in the structure. However, this difference does not impact the

short circuit current and open-circuit voltage values. Neither does it affect the trend that

we observe for both the above mentioned parameters.

A thin film Pt layer is used to form a broad-area Schottky barrier to the n-GaN layer.

However, the Pt layer does not cover the entire mesa surface; instead it is separated from

the boundaries (of the n-GaN layer) by a distance of 10 μm on both sides. The two metal

contacts, which are equidistant (60 μm) from the boundaries (of the GaN absorber layer)

are 5 μm wide. An AM0 spectrum was used for illumination.

Figure 4.7 Short-circuit current per unit length vs Pt Thickness

0.0E+00

2.0E-04

4.0E-04

6.0E-04

8.0E-04

1.0E-03

1.2E-03

1.4E-03

1.6E-03

1.8E-03

2.0E-03

0 10 20 30 40 50 60

Sho

rt C

ircu

it C

urr

ent

(A

/m)

Pt thickness (nm)

Coarse Finger

Fine Finger

48

Figure 4.7 shows a plot of the short-circuit current per unit length versus the thickness of

the Pt layer. Current density vs. voltage (J-V) curves were obtained by dividing the

calculated current per unit length by the illuminated device mesa width. The mesa width is

125 μm (50 μm) for the coarse (fine) finger case, but all other simulation parameters are

held constant. Figure 4.8 shows a plot of the short-circuit current density versus the

thickness of the Pt layer.

Figure 4.8 Short-circuit current density vs Pt Thickness

Figure 4.9 shows a zoomed-in plot of the short-circuit current density versus the thickness

of the Pt layer. It is evident from Figure 4.9 that 𝐽𝑠𝑐 is impacted by the thickness of the Pt

layer. Moreover, the short-circuit current densities are larger for the coarse finger geometry

as compared to the fine finger geometry.

0.0E+00

2.0E-04

4.0E-04

6.0E-04

8.0E-04

1.0E-03

1.2E-03

1.4E-03

0 10 20 30 40 50 60

Sho

rt C

ircu

it C

urr

ent

Den

sity

(A

/cm

2)

Pt thickness (nm)

Coarse Finger

Fine Finger

49

Figure 4.9 Short-circuit current density vs Pt Thickness (zoomed in)

The short-circuit current density is larger than in the reference case (i.e. no Pt film) for Pt

layer thicknesses up to 15 nm (fine finger) or 50 nm (coarse finger). This observation

justifies the need for a transparent conductive film. The short-circuit current density

reaches a maximum value at roughly 2 nm and 5 nm for fine finger and coarse finger

geometry, respectively. The presence of a maximum is explained by the balance of series

resistance presented by the Pt layer and its optical losses. However, for thicknesses of the

Pt layer greater than the aforementioned values for each geometry, there is a steady

decrease in the short-circuit current density. This trend suggests that after a certain

thickness, the short-circuit current density is impacted more by optical losses than by series

resistance associated with the Pt layer.

0.0E+00

2.0E-04

4.0E-04

6.0E-04

8.0E-04

1.0E-03

1.2E-03

1.4E-03

0 2 4 6 8 10 12 14

Sho

rt C

ircu

it C

urr

ent

Den

sity

(A

/cm

2)

Pt thickness (nm)

Coarse Finger

Fine Finger

50

Figure 4.10 shows a plot of the open-circuit voltage versus the thickness of the Pt layer. It

is clear that the open-circuit voltage is only weakly affected by the change in the Pt layer

thickness. The open-circuit voltage decreases by very small amounts with increasing Pt

thickness. This trend can be explained by the logarithmic dependence of the open-circuit

voltage on the short-circuit current (see Equation 2.4). Hence, the change in the thickness

of the Pt layer affects the short-circuit current, which in turn affects the open-circuit

voltage.

Figure 4.10 Open-circuit voltage vs Pt Thickness

In conclusion, computer simulations show that the use of a Pt layer increases the short-

circuit current density for Pt film thicknesses less than 15 nm (fine finger) or 50 nm (coarse

finger). Maximum short-circuit current density is achieved for a thickness of about 2 nm

and 5 nm for the fine finger and coarse finger geometries, respectively. The open-circuit

voltage is weakly affected by the change in the thickness of the Pt layer.

0.0

0.5

1.0

1.5

0 10 20 30 40 50 60

Op

en C

ircu

it V

olt

age,

Vo

c(V

)

Pt thickness (nm)

Coarse Finger

Fine Finger

51

4.3 Characterization

4.3.1 Dark & Illuminated I-V Measurements

Fabricated solar cells have been characterized by current-voltage (I-V) measurements in

the dark and under LED illumination at specific wavelengths. The three photon energies

used for illumination are as follows: 3.5 eV (Eph > Eg (GaN)), 3.15 eV (Eg (InGaN) < Eph < Eg

(GaN)) and 2.75 eV (Eph < Eg (InGaN)). The power density of these LED sources were as

follows: 100 µW/cm2, 10 mW/cm2 and 1 mW/cm2 for 3.5 eV, 3.15 eV and 2.75 eV photon

energies, respectively. These power densities were measured using a photo-detector

connected to a Newport optical meter. Additional details regarding the measurement setup

and calibration procedure can be found in Appendix A. Before, we analyze the results, it is

important to understand the sources of error in our test methodology.

4.3.2 Sources of Error

This section deals with understanding possible sources of error in our test methodology

used for electrical characterization of solar cells. A four-point measurement configuration

is used to contact the solar cell for I-V characterization. This approach is preferred over a

two-point measurement configuration because of accuracy concerns. In a two-point probe

case, the current is sourced and the voltage is measured using the same set of probes. Since

the same probes are used for both operations, the voltage drop across the wires and probes

contribute to the voltage measured by the voltmeter. The use of another set of probes to

measure the voltage separately using a high-impedance voltmeter gives more accurate

results as it only measures the voltage across the device under test (DUT).

52

Figure 4.11 I-V curves of a solar cell in the dark

Figure 4.12 I-V curves for the same solar cell under illumination

I-V measurements are subject to a number of errors which must be accounted for. Few

errors arise because experimental conditions change with every measurement. The possible

0.0E+00

1.0E-07

2.0E-07

3.0E-07

4.0E-07

5.0E-07

6.0E-07

7.0E-07

8.0E-07

9.0E-07

0.0 0.1 0.2 0.3 0.4 0.5 0.6

Cu

rren

t (A

)

Voltage (V)

Initial Test

Retest 1

Retest 2

Retest 3

Retest 4

-2.0E-08

-1.0E-08

0.0E+00

1.0E-08

2.0E-08

3.0E-08

4.0E-08

5.0E-08

0.00 0.05 0.10 0.15 0.20 0.25 0.30

Cu

rren

t (A

)

Voltage (V)

Initial Test

Retest 1

Retest 2

Retest 3

Retest 4

53

sources of error include variations in electrical probe positioning and pressure applied to

them, non-uniformity of the light beam from the light source, temperature change, external

noise and errors introduced due to the electronic instruments. In order to understand the

impact of these variations, one of the solar cell devices was measured multiple times under

dark and illuminated conditions. The dark and illuminated I-V plots are shown in Figure

4.11 and Figure 4.12. The overlapping of all the I-V curves for both cases demonstrate

good measurement reproducibility.

Figure 4.13 I-V curves of solar cells under dark and illuminated conditions

Another source of error in evaluating solar cell performance is low yield after device

fabrication. An attempt was made to reduce the consequences of low fabrication yield by

inspecting the processed wafer under a Nomarski-contrast optical microscope in order to

eliminate devices with visible defects from the measurement set. Moreover, devices that

exhibited large reverse (leakage) currents at small negative bias voltages were also

eliminated from the analysis. Such “leaky diodes” were discarded because of their unusual

-3.00E-07

-2.00E-07

-1.00E-07

0.00E+00

1.00E-07

2.00E-07

3.00E-07

-0.6 -0.4 -0.2 0.0 0.2 0.4 0.6

Cu

rren

t (A

)

Voltage (V)

Device 1 (Dark)

Device 1 (Light)

Device 2 (Dark)

Device 2 (Light)

54

behavior when tested as solar cells under LED illumination. It can be seen in Figure 4.13

that ‘Device 2’, which is one such leaky device has higher short-circuit current, lower open

circuit voltage and a smaller fill-factor compared to ‘Device 1’ (normal solar cell).

Figure 4.14 I-V curves for different InGaN/GaN-Pt solar cell devices under 395 nm LED

illumination

Even after the initial device screening described above, considerable variability remains in

the measured I-V arises for “good” solar cells distributed across the processed sample (1 x

1 cm2). Figure 4.14 shows current-voltage (I-V) curves for eight different solar cell devices

on the 10 nm Pt-InGaN/GaN solar cell sample under 395 nm LED illumination at room

temperature. This wavelength corresponds to a photon energy of 3.15 eV which will be

absorbed by the InGaN layers in the solar cell but not by the GaN layers. I-V curves having

leaky behavior or visible fabrication errors have already been eliminated from the

consideration.

0.0E+00

5.0E-09

1.0E-08

1.5E-08

2.0E-08

0.00 0.05 0.10 0.15 0.20 0.25 0.30 0.35

Cu

rren

t (A

)

Voltage (V)

55

It is observed that different devices on the same sample give different photo-response.

However, some of the variation can be explained by the fact that devices that have lower

short-circuit current have a reduced open-circuit voltage (see Equation 2.4). But, this

observation is not true for all device measured. Hence, in order to understand the variation,

same devices were illuminated with LEDs having a wavelength of 355 nm. This

wavelength corresponds to a photon energy of 3.5 eV which should be absorbed by both

GaN and InGaN layers within the material structure. Figure 4.15 shows I-V curves for the

same eight solar cells under 355nm LED illumination at room temperature.

Figure 4.15 I-V curves for different InGaN/GaN-Pt solar cell devices under 355 nm LED

illumination

With the 355 nm LED illumination, the short-circuit current was more consistent for

different devices compared to the open circuit voltage values. Variability observed for the

open-circuit voltage values may be attributable to inhomogeneity of barrier heights formed

across the sample. However, this is just speculation. It could well be some second-order

effect occurring at the metal-GaN interface which needs further investigation. One possible

0.0E+00

1.0E-08

2.0E-08

3.0E-08

4.0E-08

5.0E-08

6.0E-08

7.0E-08

8.0E-08

0.00 0.05 0.10 0.15 0.20 0.25 0.30 0.35

Cu

rren

t (A

)

Voltage (V)

56

explanation for this behavior is inhomogeneity in the quality of the InGaN absorber layer.

Table 4.1 shows average values of short-circuit current and open-circuit voltage, along with

the associated standard deviations for both 395 nm and 355 nm LED illumination.

Average value Standard Deviation

Isc (395 nm LED) 13.2 nA 1.7 nA (± 12.8%)

Isc (355 nm LED) 73.4 nA 0.8 nA (± 1.1%)

Voc (395 nm LED) 169 mV 29 mV (± 17.1%)

Voc (355 nm LED) 297 mV 15 mV (± 5.1%)

Table 4.1 Average short-circuit current and open circuit voltage values along with

standard deviation

It is evident from Table 4.1 that the standard deviations for both Jsc and Voc are almost 2x

larger for 395 nm LED illumination as compared to 355 nm LED illumination.

4.4 Experimental Results

With confidence established in our characterization techniques, and all possible sources of

error identified, we can now proceed to analyze trends in solar cell performance in relation

to the changes in the Pt layer thickness and device geometry. Figure 4.16, Figure 4.17,

Figure 4.18 and Figure 4.19 show the measured current-voltage (I-V) characteristics of

solar cells (with different geometries) with a 7 nm, 10 nm and 13 nm Pt metal film used as

the transparent conductive film under 395nm LED illumination at room temperature. It is

evident from Figure 4.16 and Figure 4.17 (for both grid style geometries) that the highest

short-circuit current is exhibited by the solar cell with a 10 nm Pt transparent conductive

film. But, the highest open-circuit voltage is exhibited by the solar cell with the 13 nm Pt

film.

57

Figure 4.16 I-V curves of InGaN/GaN-Pt coarse grid solar cell devices under 395 nm

LED illumination

Figure 4.17 I-V curves of InGaN/GaN-Pt fine grid solar cell devices under 395 nm LED

illumination

0.0E+00

2.0E-09

4.0E-09

6.0E-09

8.0E-09

1.0E-08

1.2E-08

1.4E-08

0.00 0.05 0.10 0.15 0.20 0.25 0.30 0.35 0.40 0.45

Cu

rren

t (A

)

Voltage (V)

7nm Pt

10nm Pt

13nm Pt

0.0E+00

2.0E-09

4.0E-09

6.0E-09

8.0E-09

1.0E-08

1.2E-08

1.4E-08

1.6E-08

1.8E-08

2.0E-08

0.00 0.05 0.10 0.15 0.20 0.25 0.30 0.35 0.40 0.45

Cu

rren

t (A

)

Voltage (V)

7nm Pt

10nm Pt

13nm Pt

58

Figure 4.18 I-V curves of InGaN/GaN-Pt coarse finger solar cell devices under 395 nm

LED illumination

Figure 4.19 I-V curves of InGaN/GaN-Pt fine finger solar cell devices under 395 nm

LED illumination

0.0E+00

5.0E-09

1.0E-08

1.5E-08

2.0E-08

2.5E-08

0.00 0.02 0.04 0.06 0.08 0.10 0.12 0.14 0.16 0.18 0.20

Cu

rren

t (A

)

Voltage (V)

7nm Pt

10nm Pt

13nm Pt

0.0E+00

2.0E-09

4.0E-09

6.0E-09

8.0E-09

1.0E-08

1.2E-08

1.4E-08

0.00 0.02 0.04 0.06 0.08 0.10 0.12 0.14 0.16 0.18 0.20

Cu

rren

t (A

)

Voltage (V)

7nm Pt

10nm Pt

13nm Pt

59

In the case of both finger-style geometries, it is evident from Figure 4.18 and Figure 4.19

that the highest short-circuit current and open-circuit voltage are exhibited by the solar cell

with the 10 nm Pt film. Hence, it can be concluded that the highest short-circuit current is

exhibited (for all four different geometries) by the solar cell with a 10 nm Pt film. Figure

4.20 shows the measured current-voltage (I-V) characteristics of solar cells (with different

geometries) with a 10 nm Pt film used as the transparent conductive film under 395nm

LED illumination at room temperature.

Figure 4.20 I-V curves of InGaN/GaN-Pt (10 nm) solar cell devices under 395 nm LED

illumination

Considering the different electrode geometries, there are two important parameters that

affect the short-circuit current density. The two parameters are shading losses due to the

area occupied by the opaque Ni/Ag contacts pads, and surface recombination. Key

differences in the finger and grid patterns are best illustrated by referring to Table 4.2.

0.0E+00

5.0E-09

1.0E-08

1.5E-08

2.0E-08

2.5E-08

3.0E-08

0.00 0.05 0.10 0.15 0.20 0.25

Cu

rren

t (A

)

Voltage (V)

Coarse Grid

Coarse Finger

Fine Grid

Fine Finger

60

Mesa Area (cm2) Illuminated

Area (cm2)

Bulk Volume

(cm3)

Coarse Grid 0.009604 0.008083 4.17E-7

Fine Grid 0.009604 0.007594 4.17E-7

Coarse Finger 0.013591 0.012404 5.91E-7

Fine Finger 0.011088 0.009403 4.82E-7

Table 4.2 Key differences in finger and grid patterns

Moreover, the perimeter of the mesa area for the finger patterns is larger compared to the

grid patterns. A larger perimeter results in more dangling bonds present at the surface

which act as recombination centers for minority carriers as explained previously in Section

2.1. As a result, there should be a higher probability of surface recombination in the two

finger geometries which will result in a smaller short-circuit current. High recombination

probability increases the forward diffusion current which also reduces the open-circuit

voltage. Apart from surface recombination, shading losses due to the opaque Ni/Ag contact

pads reduce the short circuit current. The four electrode geometries in decreasing order of

their respective illuminated areas are: Coarse Finger, Coarse Grid, Fine Finger and Fine

Grid. Another parameter that weakly affects the short-circuit current and open-circuit

voltage is series resistance of the contact pads.

Figure 4.20 shows the measured current-voltage (I-V) characteristics of solar cells (with

different geometries) with a 10 nm Pt film used as the transparent conductive film under

AM 1.5 spectrum illumination at room temperature. However, the sample used for the

above mentioned measurement has a different layer structure than the one mentioned

61

before. This particular sample had a layer structure which had 15 pairs of MQW (multi-

quantum well) region unlike the previous sample which had 30 pairs of MQW region.

Figure 4.21 I-V curves of InGaN/GaN-Pt solar cell devices under AM 1.5 illumination

4.5 Data Analysis and Discussion

Figure 4.22, Figure 4.23, Figure 4.24 and Figure 4.25 show the calculated current density-

voltage (J-V) characteristics of solar cells (with different geometries) with a 7 nm, 10 nm

and 13 nm Pt metal film used as the transparent conductive film under 395nm LED

illumination at room temperature. Current density vs. voltage (J-V) curves were obtained

by dividing the measured current by the illuminated device mesa area. No attempt was

made to correct for optical losses associated with reflection off the device surface. It is

evident from Figure 4.22 and Figure 4.23 (for both grid style geometries) that the highest

short-circuit current density is exhibited by the solar cell with a 10 nm Pt transparent

0.0E+00

5.0E-08

1.0E-07

1.5E-07

2.0E-07

0 0.1 0.2 0.3 0.4 0.5 0.6 0.7

Cu

rren

t (A

)

Voltage (V)

Coarse Finger

Coarse Grid

Fine Finger

Fine Grid

62

conductive film. But, the highest open-circuit voltage is exhibited by the solar cell with the

13 nm Pt film as noted previously.

Figure 4.22 J-V curves of InGaN/GaN-Pt coarse grid solar cell devices under 395 nm

LED illumination

Figure 4.23 J-V curves of InGaN/GaN-Pt fine grid solar cell devices under 395 nm LED

illumination

0.0E+00

2.0E-07

4.0E-07

6.0E-07

8.0E-07

1.0E-06

1.2E-06

1.4E-06

1.6E-06

1.8E-06

0.00 0.05 0.10 0.15 0.20 0.25 0.30 0.35 0.40 0.45

Cu

rren

t D

ensi

ty (

A/c

m2)

Voltage (V)

7nm Pt

10nm Pt

13nm Pt

0.0E+00

5.0E-07

1.0E-06

1.5E-06

2.0E-06

2.5E-06

3.0E-06

0.00 0.05 0.10 0.15 0.20 0.25 0.30 0.35 0.40

Cu

rren

t D

ensi

ty (

A/c

m2)

Voltage (V)

7nm Pt

10nm Pt

13nm Pt

63

Figure 4.24 J-V curves of InGaN/GaN-Pt coarse finger solar cell devices under 395 nm

LED illumination

Figure 4.25 J-V curves of InGaN/GaN-Pt fine finger solar cell devices under 395 nm

LED illumination

0.0E+00

2.0E-07

4.0E-07

6.0E-07

8.0E-07

1.0E-06

1.2E-06

1.4E-06

1.6E-06

1.8E-06

2.0E-06

0.00 0.02 0.04 0.06 0.08 0.10 0.12 0.14 0.16 0.18 0.20

Cu

rren

t D

ensi

ty (

A/c

m2)

Voltage (V)

7nm Pt

10nm Pt

13nm Pt

0.0E+00

2.0E-07

4.0E-07

6.0E-07

8.0E-07

1.0E-06

1.2E-06

1.4E-06

1.6E-06

0.00 0.02 0.04 0.06 0.08 0.10 0.12 0.14

Cu

rren

t D

ensi

ty (

A/c

m2)

Voltage (V)

7nm Pt

10nm Pt

13nm Pt

64

It is evident from Figure 4.24 and Figure 4.25 that the highest short-circuit current density

and open-circuit voltage are exhibited by the solar cell with the 10 nm Pt film. Hence, it

can be concluded that the highest short-circuit current density is exhibited (for all four

different geometries) by the solar cell with a 10 nm Pt film. Figure 4.26 shows the

measured current density-voltage (J-V) characteristics of solar cells (with different

geometries) with a 10 nm Pt film used as the transparent conductive film under 395nm

LED illumination at room temperature.

Figure 4.26 J-V curve of InGaN/GaN-Pt (10 nm) solar cell devices under 395 nm LED

illumination

Figure 4.27 shows the measured current density-voltage (J-V) characteristics of solar cells

(with different geometries) with a 10 nm Pt film used as the transparent conductive film

under AM 1.5 spectrum illumination at room temperature. As noted before, the above

mentioned measurements were made on a sample with a different layer structure (explained

previously in this section).

0.0E+00

5.0E-07

1.0E-06

1.5E-06

2.0E-06

2.5E-06

3.0E-06

0.00 0.05 0.10 0.15 0.20 0.25

Cu

rren

t D

ensi

ty (

A/c

m2)

Voltage (V)

Coarse Grid

Coarse Finger

Fine Grid

Fine Finger

65

Figure 4.27 J-V curves of InGaN/GaN-Pt solar cell devices under AM 1.5 illumination

The key device metrics Jsc and Voc for the three solar cells with Pt thicknesses of 7 nm, 10

nm and 13 nm are plotted in Figure 4.28 and Figure 4.29 as function of the thickness of Pt

film. It is evident from Figure 4.28 that the short-circuit current density shows a consistent

overall trend independent of the device geometry and top-side electrode pitch. The short-

circuit current density is maximum for all four geometries for a thickness of 10 nm of Pt.

This can be explained by looking at the electrical and optical properties of the Pt films. The

sheet resistance of the Pt film decreases with increase in Pt thickness which improves its

ability to efficiently collect carriers. On the other hand, the optical transmission of the Pt

film decreases with increase in Pt thickness which reduces the amount of light passing

though it to reach the absorber layer. Since, the increase of thickness has two opposite

effects on the short-circuit current density, thus, the current is maximized for an optimized

0.0E+00

2.0E-06

4.0E-06

6.0E-06

8.0E-06

1.0E-05

1.2E-05

1.4E-05

1.6E-05

1.8E-05

0 0.1 0.2 0.3 0.4 0.5 0.6 0.7

Cu

rren

t D

ensi

ty (

A/c

m2)

Voltage (V)

Coarse Grid

Coarse Finger

Fine Grid

Fine Finger

66

thickness of Pt which happens to be 10 nm for this case. The non-monotonic behavior is

also consistent with the APSYS simulation as shown in Figure 4.8.

Figure 4.28 Short circuit current density as a function of Pt thickness

Figure 4.29 shows the open-circuit voltage of a solar cell as function of the thickness of Pt

film used in the solar cell. No particular trend was observed between the open-circuit

voltage and the Pt thickness of the film. However, the open-circuit voltage has a

logarithmic dependence on the short-circuit current. Hence, small changes in short-circuit

current should not affect the open-circuit voltage as seen in the APSYS simulation. As

postulated before, this behavior of the open circuit voltage can be attributed to

inhomogeneity of barrier heights formed across the sample; or it could be some second

order effect occurring at the Pt-GaN interface. Another inference that can be drawn from

the data above is that the finger geometries consistently exhibit a smaller open circuit

0.0E+00

5.0E-07

1.0E-06

1.5E-06

2.0E-06

2.5E-06

3.0E-06

6 7 8 9 10 11 12 13 14

Sho

rt C

ircu

it C

urr

ent

Den

sity

(A

/cm

2)

Platinum Thickness (nm)

Coarse Grid

Coarse Finger

Fine Grid

Fine Fingers

67

voltage compared to the grid geometries. This behavior is explained through a higher

surface recombination probability in the finger geometries as mentioned before in the

previous section, which reduces the open-circuit voltage.

Figure 4.29 Open-circuit voltage as a function of Pt thickness

Another important observation is that these solar cells exhibit a higher short-circuit current

density when illuminated by 355 nm LED source. This makes InGaN Schottky solar cells

well suited for space applications where UV light is abundant. These solar cell devices

were also illuminated with a 455 nm LED source which did not produce any photocurrent

confirming that photons below the band gap of InGaN do not get absorbed.

0.00

0.05

0.10

0.15

0.20

0.25

0.30

0.35

0.40

0.45

6 7 8 9 10 11 12 13 14

Op

en C

ircu

it V

olt

age

(V)

Platinum Thickness (nm)

Coarse Grid

Coarse Finger

Fine Grid

Fine Fingers

68

We report on Pt/InGaN/GaN Schottky barrier solar cells with different thicknesses of

Platinum which is being used as the transparent conductive film. Each solar cell with a

different thickness of Platinum has four different electrode geometries. Relationship

between solar cell performance and Pt thickness is established and explained. The impact

of the contact pad geometries on the short circuit-current density and open-circuit voltage

is also studied. The results show that the photovoltaic behavior of InGaN based Schottky

solar cells is found to be affected by the properties of the transparent conducting layer and

the contact design. Hence, it is essential to optimize transparency and conductivity of the

transparent conductive layer and contact pad in order to efficiently collect photo-carriers.

The present work can be an important step towards further study of InGaN based Schottky

solar cells.

69

Chapter 5. Summary and Conclusions

Thin film solar cells made from InGaN are of considerable interest because this material

system covers an unusually wide energy range (from 3.4 eV for GaN to 0.7 eV for InN),

has high optical absorption coefficients, and exhibits better radiation hardness than

conventional III-V semiconductors. Recently, several groups have investigated InGaN

based homo-junction and hetero-junction solar cells most of which employ a p-i-n structure

to enable more efficient carrier collection. However, there have been very few reports on

well-conducting p-type InGaN with higher indium content such as would be necessary to

make p-i-n InGaN solar cells with band gaps in the range 1.9 to 1.0 eV. The issue of p-type

doping and finding a suitable p-type contact for GaN was averted in this present work by

introducing a novel Schottky solar cell structure. Moreover, thin transparent conductive

films made of Pt were placed in contact with n-type InGaN/GaN heterostructures to

demonstrate the feasibility of InGaN Schottky barrier solar cells. We report on the

feasibility of InGaN/GaN-Pt Schottky solar cells with different thickness of Pt (7 nm, 10

nm and 13 nm) and four different contact pad schemes. Thin films of Pt deposited on

double side polished sapphire with thicknesses of 7 nm, 10 nm and 13 nm were

characterized via TLM measurements and optical transmission measurements. TLM

measurements showed the following results: sheet resistance of 103.9 Ω/sq., 57 Ω/sq. and

41.5 Ω/sq. for 7 nm, 10 nm and 13 nm Pt thickness films respectively. These results

demonstrated that the sheet resistance decreased with increase in Pt thickness, which is

expected. These results also demonstrate the ability of the electron-beam deposition system

to accurately deposit thin films with at least a 3 nm accuracy. We observed a strong

dependence of the transmission spectrum on the platinum thickness. The optical

70

transmission properties of the Pt films increased as the Pt thickness was decreased. The

transmission results again confirm our ability to accurately deposit thin films. The results

also show the ability of the Filmetrics measurement system to resolve transmission

difference associated with thin films with such precision.

Simulations were carried out using Crosslight APYS to investigate the impact of thickness

of the Pt TCO layer on the performance of GaN based solar cells. The dependence of short-

circuit current and open-circuit voltage on the thickness of the Pt film was studied using

simulations. Solar cell measurements were made in the dark and with LED illumination

(395 nm) using a Keithley I-V sweep tool and a four-point probe measurement setup.

Possible sources of error arising due to measurement setup were evaluated and were shown

to cause negligible impact on the measurements. Errors arising due to variation in

fabrication were addressed by eliminating devices with visible fabrication errors and the

ones with high saturation current suggesting leaky behavior from the analysis. Sample

variability was attributed to variation in the quality of InGaN film grown. An effort was

made to address this issue, however, further investigation is required. Solar cells with 10

nm Pt as the transparent conductive film exhibited highest short circuit current density for

all four types of contact pad patterns. This result is explained by optimization of the sheet

resistance and transmission spectrum for the 10 nm film which enables more efficient

carrier collection as compared to the solar cells with the 7 nm and 13 nm Pt films. However,

no such relationship was observed between the open circuit voltage and the Pt thickness.

This behavior of the open circuit voltage can be attributed to inhomogeneity of barrier

heights formed across the sample; or it could be some second order effect occurring at the

71

Pt-GaN interface. Solar cells with the 10 nm Pt film with different contact geometries was

analyzed in detail. Parameters such as surface recombination, area occupied by the opaque

contact pads and series resistance are found to be responsible for affecting the short-circuit

current density and open circuit voltage. Schottky barrier solar cells made with Pt exhibited

higher short circuit currents when illuminated with a UV LED source (355 nm) as

compared to the 395 nm LED source which confirms that Schottky barrier solar cells give

better spectral response for high energy photons which are absorbed in the near depletion

regions. From our study, it has been found that the optimized thickness of the Pt film for

our Schottky barrier solar cell is 10 nm. This present work could be a significant step for

further study of InGaN-GaN Schottky barrier solar cells.

This present work helps us in understanding the impact of the contact scheme employed in

InGaN based Schottky barrier solar cells which can be utilized to improve the performance

of InGaN Schottky barrier solar cells fabricated with different transparent conductive films.

New materials like transparent conducting oxides need to be investigated in order to obtain

contacts that offer higher transmission and lower sheet resistance. An effort has been made

to optimize the grid or layer contact pad on top of the transparent conductive film.

However, more optimization work still remains to be done. In summary, Pt/GaN/InGaN

Schottky barrier solar cells have been investigated.

72

Appendix A. I-V Measurement Setup

The apparatus used to make “4-wire” I-V measurements for both TLM measurements and

solar cell characterization is shown in Figure A.1. A Keithley 2400 SMU (Source-Measure

unit) is used to source current/voltage and also probe current/voltage. The use of the SMUs

has simplified device characterization that once required multiple programmable power

supplies and digital multi-meters. The Model 2400’s ability to source/sink up to 1A with

0.5% accuracy or better and its low noise, high impedance offers a simple cost effective

alternative for PV cell characterization. The Model 2400 offers 10μV resolution on the 2V

range and 100μV on the 20V range which is sufficient to accurately measure the I-V curve

of any solar cell. The Model 2400’s can measure low currents in the 1mA range with 10pA

maximum resolution which is sufficient for virtually all dark I-V applications.

Figure A.1 I-V Measurement Apparatus Setup

A computer is used to carry out individual measurements and to collect the experimental

data. A LabVIEW program is used control the Keithley 2400 source-measure meter to

carry out a voltage or current sweep in specified intervals with either linear and logarithmic

sweeps over the desired current or voltage ranges. The program also plots I-V

73

characteristics for the user to analyze. The measurements also get saved locally on the

computer, which can be later on used for analysis. The Keithley 2400, although already

calibrated initially by the manufacturer, was calibrated again as a part of the setup in order

to determine inaccuracies in measurements due to the apparatus itself. For this, a short

circuit test was conducted, which is performed by shorting out the probes in the four point

measurement setup to determine the external resistances due to the probes and wires used

in the setup. The value determined from this test was subtracted from actual tests to get

more accurate results. All I-V measurements in this work were done using the setup

described above.

74

REFERENCES

[1] U. S. E. I. Administration, "International Energy Outlook 2013," ed, 2013.

[2] N. O. A. Administration, "Trends in Atmospheric Carbon Dioxide," ed, 2014.

[3] M. Loster, "Total Primary Energy Supply— From Sunlight," ed, 2010.

[4] R. L. Cummerow, "Photovoltaic Effect in p-n Junctions," Physical Review, vol.

95, pp. 16-21, 07/01/ 1954.

[5] J. Nelson, The Physics of Solar Cells. UK: Imperial College Press, 2003.

[6] D. M. Chapin, C. S. Fuller, and G. L. Pearson, "A New Silicon p‐n Junction

Photocell for Converting Solar Radiation into Electrical Power," Journal of

Applied Physics, vol. 25, pp. 676-677, 1954.

[7] C. Honsberg and S. Bowden. Available:

http://www.pveducation.org/pvcdrom/introduction/introduction

[8] R. W. Miles, K. M. Hynes, and I. Forbes, "Photovoltaic solar cells: An overview

of state-of-the-art cell development and environmental issues," Progress in

Crystal Growth and Characterization of Materials, vol. 51, pp. 1-42, // 2005.

[9] G. Masson, M. Latour, M. Rekinger, I.-T. Theologitis, and M. Papoutsi, "Global

Market Outlook for Photovoltaics 2013-2017," European Photovoltaic Industry

Association.

[10] Solar Energy Market Growth. Available: http://www.solarbuzz.com/facts-and-

figures/markets-growth/market-growth

[11] M. A. Green, Third Generation Photovoltaics: Advanced Solar Electricity

Generation,”. Berlin: Springer-Verlag, 2003.

[12] Best Research Cell Efficiencies. Available: http://www.nrel.gov/ncpv/

[13] M. A. Green, K. Emery, Y. Hishikawa, W. Warta, and E. D. Dunlop, "Solar cell

efficiency tables (version 43)," Progress in Photovoltaics: Research and

Applications, vol. 22, pp. 1-9, 2014.

[14] A. Barnett, D. Kirkpatrick, C. Honsberg, D. Moore, M. Wanlass, K. Emery, et al.,

"Milestones toward 50% efficient solar cell modules," presented at the Proc. of

22nd European PV Solar Energy Conference, Milan, Italy,.

[15] W. Shockley and H. J. Queisser, "Detailed Balance Limit of Efficiency of p‐n

Junction Solar Cells," Journal of Applied Physics, vol. 32, pp. 510-519, 1961.

75

[16] C. Honsberg, O. Jani, A. Doolittle, E. Trybus, G. Namkoong, I. Ferguson, et al.,

"InGaN – A New Solar Cell Material," in Proceedings of the 19th European

Photovoltaic Science and Engineering Conference, Paris, France, pp. 15-20.

[17] O. K. Jani, "Development of wide-band gap InGaN solar cells for high efficiency

photovoltaics," Ph.D. dissertation, Electrical and Computer Engineering

Department, Georgia Institute of Technology, 2008.

[18] J. Wu and W. Walukiewicz, "Band gaps of InN and group III nitride alloys,"

Superlattices and Microstructures, vol. 34, pp. 63-75, 7// 2003.

[19] J. Wu, W. Walukiewicz, K. M. Yu, J. W. Ager, E. E. Haller, H. Lu, et al., "Small

band gap bowing in In[sub 1−x]Ga[sub x]N alloys," Applied Physics Letters, vol.

80, p. 4741, 2002.

[20] J. Wu, W. Walukiewicz, K. M. Yu, W. Shan, J. W. Ager, E. E. Haller, et al.,

"Superior radiation resistance of In[sub 1−x]Ga[sub x]N alloys: Full-solar-

spectrum photovoltaic material system," Journal of Applied Physics, vol. 94, p.

6477, 2003.

[21] S. Nakamura, T. Mukai, and M. Senoh, "Candela‐class high‐brightness

InGaN/AlGaN double‐heterostructure blue‐light‐emitting diodes," Applied

Physics Letters, vol. 64, pp. 1687-1689, 1994.

[22] S. Nakamura, M. Senoh, N. Iwasa, and S.-i. Nagahama, "High-Brightness InGaN

Blue, Green and Yellow Light-Emitting Diodes with Quantum Well Structures,"

Jpn. J. Appl. Phys., vol. 34, pp. L 797-L 799, 1995.

[23] S. Nakamura, M. Senoh, S.-i. Nagahama, N. Iwasa, T. Yamada, T. Matsushita, et

al., "Room-temperature continuous-wave operation of InGaN multi-quantum-

well-structure laser diodes with a long lifetime," Applied Physics Letters, vol. 70,

pp. 868-870, 1997.

[24] W. Yong, Z. Yonggang, M. Xiaohui, Y. Naisen, D. Dongmei, and L. Kei May,

"Progress on the GaN-based LEDs and LDs," in Optoelectronics and

Microelectronics (ICOM), 2012 International Conference on, 2012, pp. 105-110.

[25] E. Trybus, O. Jani, S. Burnham, I. Ferguson, C. Honsberg, M. Steiner, et al.,

"Characteristics of InGaN designed for photovoltaic applications," physica status

solidi (c), vol. 5, pp. 1843-1845, 2008.

76

[26] X. Zheng, R.-H. Horng, D.-S. Wuu, M.-T. Chu, W.-Y. Liao, M.-H. Wu, et al.,

"High-quality InGaN∕GaN heterojunctions and their photovoltaic effects," Applied

Physics Letters, vol. 93, p. 261108, 2008.

[27] M. Anani, H. Abid, Z. Chama, C. Mathieu, A. Sayede, and B. Khelifa,

"InxGa1−xN refractive index calculations," Microelectronics Journal, vol. 38, pp.

262-266, 2// 2007.

[28] J. Wu, "When group-III nitrides go infrared: New properties and perspectives,"

Journal of Applied Physics, vol. 106, pp. -, 2009.

[29] O. Jani, I. Ferguson, C. Honsberg, and S. Kurtz, "Design and characterization of

GaN∕InGaN solar cells," Applied Physics Letters, vol. 91, p. 132117, 2007.

[30] F. Bernardini and V. Fiorentini, "Spontaneous versus Piezoelectric Polarization in

III–V Nitrides: Conceptual Aspects and Practical Consequences," physica status

solidi (b), vol. 216, pp. 391-398, 1999.

[31] F. Bernardini and V. Fiorentini, "Nonlinear macroscopic polarization in III-V

nitride alloys," Physical Review B, vol. 64, p. 085207, 08/08/ 2001.

[32] S. Nakamura and T. Mukai, "High Quality InGaN Films grown on GaN Films,"

Jpn. J. Appl. Phys., vol. 31, pp. L 1457-L 1459, 1992.

[33] X.-m. Cai, S.-w. Zeng, and B.-p. Zhang, "Fabrication and characterization of

InGaN p-i-n homojunction solar cell," Applied Physics Letters, vol. 95, p. 173504,

2009.

[34] X. Chen, K. D. Matthews, D. Hao, W. J. Schaff, and L. F. Eastman, "Growth,

fabrication, and characterization of InGaN solar cells," physica status solidi (a),

vol. 205, pp. 1103-1105, 2008.

[35] C. J. Neufeld, N. G. Toledo, S. C. Cruz, M. Iza, S. P. DenBaars, and U. K.

Mishra, "High quantum efficiency InGaN/GaN solar cells with 2.95 eV band

gap," Applied Physics Letters, vol. 93, p. 143502, 2008.

[36] E. Matioli, C. Neufeld, M. Iza, S. C. Cruz, A. A. Al-Heji, X. Chen, et al., "High

internal and external quantum efficiency InGaN/GaN solar cells," Applied Physics

Letters, vol. 98, p. 021102, 2011.

[37] J. R. Lang, C. J. Neufeld, C. A. Hurni, S. C. Cruz, E. Matioli, U. K. Mishra, et al.,

"High external quantum efficiency and fill-factor InGaN/GaN heterojunction

77

solar cells grown by NH[sub 3]-based molecular beam epitaxy," Applied Physics

Letters, vol. 98, p. 131115, 2011.

[38] C. J. Neufeld, C. Zhen, S. C. Cruz, N. G. Toledo, S. P. DenBaars, and U. K.

Mishra, "Optimization of the p-GaN window layer for InGaN/GaN solar cells," in

Photovoltaic Specialists Conference (PVSC), 2010 35th IEEE, 2010, pp. 002089-

002092.

[39] O. Jani, C. Honsberg, Y. Huang, J. O. Song, I. Ferguson, G. Namkoong, et al.,

"Design, Growth, Fabrication and Characterization of High-Band Gap

InGaN/GaN Solar Cells," in Photovoltaic Energy Conversion, Conference Record

of the 2006 IEEE 4th World Conference on, 2006, pp. 20-25.

[40] O. Jani, B. Jampana, M. Mehta, H. Yu, I. Ferguson, R. Opila, et al.,

"Optimization of GaN window layer for InGaN solar cells using polarization

effect," in Photovoltaic Specialists Conference, 2008. PVSC '08. 33rd IEEE,

2008, pp. 1-4.

[41] O. Jani, C. Honsberg, A. Asghar, D. Nicol, I. Ferguson, A. Doolittle, et al.,

"Characterization and analysis of InGaN photovoltaic devices," in Photovoltaic

Specialists Conference, 2005. Conference Record of the Thirty-first IEEE, 2005,

pp. 37-42.

[42] H. Ray-Hua, L. Shih-Ting, T. Yu-Li, C. Mu-Tao, L. Wen-Yih, W. Ming-Hsien, et

al., "Improved Conversion Efficiency of GaN/InGaN Thin-Film Solar Cells,"

Electron Device Letters, IEEE, vol. 30, pp. 724-726, 2009.

[43] L. Hsu and W. Walukiewicz, "Modeling of InGaN/Si tandem solar cells," Journal

of Applied Physics, vol. 104, p. 024507, 2008.

[44] A. R. Lothar, G. Iulian, Y. Kin Man, M. K. Vincent, W. Wladek, and W. A. Joel,

III, "Demonstration of a III–Nitride/Silicon Tandem Solar Cell," Applied Physics

Express, vol. 2, p. 122202, 2009.

[45] R. Dahal, B. Pantha, J. Li, J. Y. Lin, and H. X. Jiang, "InGaN/GaN multiple

quantum well solar cells with long operating wavelengths," Applied Physics

Letters, vol. 94, p. 063505, 2009.

78

[46] R. Dahal, J. Li, K. Aryal, J. Y. Lin, and H. X. Jiang, "InGaN/GaN multiple

quantum well concentrator solar cells," Applied Physics Letters, vol. 97, p.

073115, 2010.

[47] S. Jinn-Kong, Y. Chih-Ciao, T. Shang-Ju, C. Kuo-Hua, L. Ming-Lun, W.-C. Lai,

et al., "Demonstration of GaN-Based Solar Cells With GaN/InGaN Superlattice

Absorption Layers," Electron Device Letters, IEEE, vol. 30, pp. 225-227, 2009.

[48] A. Bhuiyan, K. Sugita, A. Hashimoto, and A. Yamamoto, "InGaN Solar Cells:

Present State of the Art and Important Challenges," Photovoltaics, IEEE Journal

of, vol. 2, pp. 276-293, 2012.

[49] J. Xue, D. Chen, B. Liu, Z. Xie, R. Jiang, R. Zhang, et al., "Au/Pt/InGaN/GaN

Heterostructure Schottky Prototype Solar Cell," Chin. Phys. Lett., vol. 26, 2009.

[50] S. Lin, B. P. Zhang, S. W. Zeng, X. M. Cai, J. Y. Zhang, S. X. Wu, et al.,

"Preparation and properties of Ni/InGaN/GaN Schottky barrier photovoltaic

cells," Solid-State Electronics, vol. 63, pp. 105-109, 9// 2011.

[51] C. Wang and R. F. Davis, "Deposition of highly resistive, undoped, and p‐type,

magnesium‐doped gallium nitride films by modified gas source molecular beam

epitaxy," Applied Physics Letters, vol. 63, pp. 990-992, 1993.

[52] X. Guo and E. F. Schubert, "Current crowding in GaN/InGaN light emitting

diodes on insulating substrates," Journal of Applied Physics, vol. 90, p. 4191,

2001.

[53] X. Zheng, L. Tang, D. Zhang, J. Dong, and H. Yang, "Effect of contact spreading

layer on photovoltaic response of InGaN-based solar cells," physica status solidi

(a), vol. 208, pp. 199-201, 2011.

[54] X. M. Cai, Y. Wang, Z. D. Li, X. Q. Lv, J. Y. Zhang, L. Y. Ying, et al.,

"Improved photovoltaic performance of InGaN/GaN solar cells with optimized

transparent current spreading layers," Applied Physics A, vol. 111, pp. 483-486,

2013.

[55] J.-P. Shim, J. Seong-Ran, J. Yon-Kil, and D.-S. Lee, "Improved Efficiency by

Using Transparent Contact Layers in InGaN-Based p-i-n Solar Cells," Electron

Device Letters, IEEE, vol. 31, pp. 1140-1142, 2010.

[56] E. H. Rhoderick, Metal-Semiconductor Contacts: Oxford University Press, 1978.

79

[57] Q. Z. Liu and S. S. Lau, "A review of the metal–GaN contact technology," Solid-

State Electronics, vol. 42, pp. 677-691, 5/6/ 1998.

[58] J.-K. Ho, C.-S. Jong, C. C. Chiu, C.-N. Huang, C.-Y. Chen, and K.-K. Shih,

"Low-resistance ohmic contacts to p-type GaN," Applied Physics Letters, vol. 74,

p. 1275, 1999.

[59] J.-K. Ho, C.-S. Jong, C. C. Chiu, C.-N. Huang, K.-K. Shih, L.-C. Chen, et al.,

"Low-resistance ohmic contacts to p-type GaN achieved by the oxidation of

Ni/Au films," Journal of Applied Physics, vol. 86, p. 4491, 1999.

[60] J. M. Essick and R. T. Mather, "Characterization of a bulk semiconductor’s band

gap via a near‐absorption edge optical transmission experiment," American

Journal of Physics, vol. 61, pp. 646-649, 1993.

[61] K. M. Yu, M. A. Mayer, D. T. Speaks, H. He, R. Zhao, L. Hsu, et al., "Ideal

transparent conductors for full spectrum photovoltaics," Journal of Applied

Physics, vol. 111, pp. -, 2012.

[62] T. Koida, H. Sai, H. Shibata, and M. Kondo, "Trend of transparent conductive

oxides for solar cells," in Active-Matrix Flatpanel Displays and Devices (AM-

FPD), 2012 19th International Workshop on, 2012, pp. 45-48.

[63] D. S. Ginley and C. Bright, "Transparent Conducting Oxides," MRS Bulletin, vol.

25, pp. 15-18, 2000.

[64] D. S. Ginley and J. D. Perkins, Handbook of Transparent Conductors. New York:

Springer Science+Business, 2010.

[65] G. K. Reeves and H. B. Harrison, "Obtaining the specific contact resistance from

transmission line model measurements," Electron Device Letters, IEEE, vol. 3,

pp. 111-113, 1982.